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27006, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26088, + "max_open": 22089, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26015, + "max_open": 22016, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31337, + "max_open": 27338, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31122, + "max_open": 27123, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..e530479ad5f8a2d94b235d4641c311820985a8a6 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=5 evals=25 maxopen=19) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_5 (solved pops=56 evals=368 maxopen=313) +[OK ] extrinsic_L0_6 (solved pops=57 evals=353 maxopen=297) +[OK ] extrinsic_L0_3 (solved pops=61 evals=368 maxopen=308) +[OK ] extrinsic_L0_7 (solved pops=56 evals=356 maxopen=301) +[OK ] extrinsic_L0_10 (solved pops=7 evals=41 maxopen=35) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=20 evals=152 maxopen=133) +[OK ] extrinsic_L0_9 (solved pops=50 evals=327 maxopen=278) +[OK ] extrinsic_L0_8 (solved pops=58 evals=361 maxopen=304) +[OK ] extrinsic_L0_4 (solved pops=206 evals=1114 maxopen=909) +[OK ] extrinsic_L1_4 (solved pops=16 evals=116 maxopen=99) +[OK ] extrinsic_L0_11 (solved pops=208 evals=1124 maxopen=917) +[OK ] extrinsic_L1_1 (solved pops=214 evals=1155 maxopen=942) +[OK ] extrinsic_L1_2 (solved pops=461 evals=2467 maxopen=2007) +[OK ] extrinsic_L1_3 (solved pops=461 evals=2464 maxopen=2004) +[OK ] extrinsic_L2_1 (solved pops=1255 evals=6827 maxopen=5573) +[OK ] extrinsic_L2_6 (solved pops=1581 evals=9164 maxopen=7584) +[OK ] extrinsic_L2_7 (solved pops=999 evals=5573 maxopen=4575) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26089 maxopen=22090) +[OK ] extrinsic_L0_14 (solved pops=3997 evals=26361 maxopen=22365) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25961 maxopen=21962) +[OK ] extrinsic_L2_11 (solved pops=22 evals=145 maxopen=122) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25956 maxopen=21957) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25801 maxopen=21802) +[OK ] extrinsic_L2_9 (solved pops=1002 evals=5617 maxopen=4616) +[OK ] extrinsic_L2_12 (solved pops=1369 evals=7783 maxopen=6415) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26033 maxopen=22034) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26421 maxopen=22422) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25833 maxopen=21834) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25962 maxopen=21963) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25843 maxopen=21844) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25862 maxopen=21863) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26019 maxopen=22020) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26019 maxopen=22020) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25802 maxopen=21803) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25949 maxopen=21950) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25981 maxopen=21982) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26138 maxopen=22139) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25955 maxopen=21956) +[ ] extrinsic_L3_11 (budget pops=4000 evals=26180 maxopen=22181) +[OK ] extrinsic_L3_13 (solved pops=3442 evals=21594 maxopen=18153) +[OK ] extrinsic_L3_14 (solved pops=3143 evals=19167 maxopen=16025) +[ ] extrinsic_L3_12 (budget pops=4000 evals=26181 maxopen=22182) +[ ] extrinsic_L3_15 (budget pops=4000 evals=25975 maxopen=21976) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26013 maxopen=22014) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25760 maxopen=21761) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25900 maxopen=21901) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26010 maxopen=22011) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26116 maxopen=22117) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26117 maxopen=22118) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25919 maxopen=21920) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26272 maxopen=22273) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26160 maxopen=22161) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25902 maxopen=21903) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26648 maxopen=22649) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26284 maxopen=22285) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25815 maxopen=21816) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26132 maxopen=22133) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26832 maxopen=22833) +[ ] extrinsic_L4_2 (budget pops=4000 evals=25903 maxopen=21904) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26088 maxopen=22089) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25953 maxopen=21954) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25955 maxopen=21956) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26104 maxopen=22105) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26766 maxopen=22767) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26233 maxopen=22234) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26734 maxopen=22735) +[OK ] extrinsic_L4_12 (solved pops=1305 evals=7204 maxopen=5897) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25355 maxopen=21356) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26260 maxopen=22261) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25890 maxopen=21891) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26328 maxopen=22329) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26321 maxopen=22322) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26251 maxopen=22252) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26322 maxopen=22323) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26288 maxopen=22289) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26563 maxopen=22564) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26097 maxopen=22098) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26504 maxopen=22505) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26444 maxopen=22445) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26261 maxopen=22262) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26637 maxopen=22638) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31384 maxopen=27385) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25972 maxopen=21973) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31299 maxopen=27300) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31247 maxopen=27248) +[ ] extrinsic_L6_4 (budget pops=4000 evals=31136 maxopen=27137) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31005 maxopen=27006) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26088 maxopen=22089) +[ ] extrinsic_L6_7 (budget pops=4000 evals=26015 maxopen=22016) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31337 maxopen=27338) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31122 maxopen=27123) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json +Solved 27/94 in 2748.4s diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json 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"budget", + "pops_used": 4000, + "evals_used": 26146, + "max_open": 22147, + "solution_actions": null, + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26276, + "max_open": 22277, + "solution_actions": null, + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26322, + "max_open": 22323, + "solution_actions": null, + "problem": "extrinsic_L5_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26665, + "max_open": 22666, + "solution_actions": null, + "problem": "extrinsic_L5_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26566, + "max_open": 22567, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31108, + "max_open": 27109, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25820, + "max_open": 21821, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31119, + "max_open": 27120, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31128, + "max_open": 27129, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30893, + "max_open": 26894, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30855, + "max_open": 26856, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25854, + "max_open": 21855, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25725, + "max_open": 21726, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31215, + "max_open": 27216, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31110, + "max_open": 27111, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..6764d42b04004a06df2c0e39f41cea94a4fc423f --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_5 (solved pops=53 evals=321 maxopen=269) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_3 (solved pops=81 evals=461 maxopen=381) +[OK ] extrinsic_L0_9 (solved pops=47 evals=324 maxopen=262) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_8 (solved pops=53 evals=349 maxopen=297) +[OK ] extrinsic_L0_6 (solved pops=51 evals=316 maxopen=266) +[OK ] extrinsic_L0_7 (solved pops=55 evals=354 maxopen=300) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=21 evals=167 maxopen=147) +[OK ] extrinsic_L0_4 (solved pops=214 evals=1162 maxopen=949) +[OK ] extrinsic_L1_4 (solved pops=17 evals=105 maxopen=87) +[OK ] extrinsic_L0_11 (solved pops=216 evals=1171 maxopen=956) +[OK ] extrinsic_L1_1 (solved pops=216 evals=1179 maxopen=946) +[OK ] extrinsic_L1_2 (solved pops=511 evals=2775 maxopen=2265) +[OK ] extrinsic_L1_3 (solved pops=511 evals=2772 maxopen=2262) +[OK ] extrinsic_L2_1 (solved pops=1267 evals=6975 maxopen=5709) +[OK ] extrinsic_L2_6 (solved pops=1665 evals=9709 maxopen=8045) +[OK ] extrinsic_L2_7 (solved pops=979 evals=5549 maxopen=4571) +[OK ] extrinsic_L0_14 (solved pops=3924 evals=25896 maxopen=21973) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26030 maxopen=22031) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25892 maxopen=21893) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25885 maxopen=21886) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25689 maxopen=21690) +[OK ] extrinsic_L2_9 (solved pops=971 evals=5469 maxopen=4499) +[OK ] extrinsic_L2_12 (solved pops=1216 evals=6736 maxopen=5521) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26366 maxopen=22367) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26159 maxopen=22160) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25751 maxopen=21752) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25890 maxopen=21891) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25724 maxopen=21725) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25765 maxopen=21766) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25849 maxopen=21850) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25842 maxopen=21843) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25690 maxopen=21691) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25843 maxopen=21844) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25997 maxopen=21998) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26077 maxopen=22078) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25928 maxopen=21929) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25861 maxopen=21862) +[OK ] extrinsic_L3_14 (solved pops=3108 evals=19169 maxopen=16062) +[OK ] extrinsic_L3_13 (solved pops=3498 evals=22590 maxopen=19093) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25866 maxopen=21867) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26017 maxopen=22018) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26009 maxopen=22010) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25758 maxopen=21759) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25576 maxopen=21577) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25793 maxopen=21794) +[ ] extrinsic_L3_20 (budget pops=4000 evals=25871 maxopen=21872) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25881 maxopen=21882) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25825 maxopen=21826) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26191 maxopen=22192) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26160 maxopen=22161) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26047 maxopen=22048) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26907 maxopen=22908) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26054 maxopen=22055) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25913 maxopen=21914) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26091 maxopen=22092) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26713 maxopen=22714) +[ ] extrinsic_L4_3 (budget pops=4000 evals=25875 maxopen=21876) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26947 maxopen=22948) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25805 maxopen=21806) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26110 maxopen=22111) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25825 maxopen=21826) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26759 maxopen=22760) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26366 maxopen=22367) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25831 maxopen=21832) +[OK ] extrinsic_L4_12 (solved pops=1249 evals=7180 maxopen=5929) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25750 maxopen=21751) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26316 maxopen=22317) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25916 maxopen=21917) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26306 maxopen=22307) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26000 maxopen=22001) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26127 maxopen=22128) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26200 maxopen=22201) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25999 maxopen=22000) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26146 maxopen=22147) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26479 maxopen=22480) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26276 maxopen=22277) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26322 maxopen=22323) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26665 maxopen=22666) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26566 maxopen=22567) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25820 maxopen=21821) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31108 maxopen=27109) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31119 maxopen=27120) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30893 maxopen=26894) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31128 maxopen=27129) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30855 maxopen=26856) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25854 maxopen=21855) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25725 maxopen=21726) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31110 maxopen=27111) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31215 maxopen=27216) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P 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'P] -> (iff 'P 'Q)]) -> false])) [false -> ('P : prop) -> 'P]); [(or [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false])) -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a or_il", + "=> .", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false])) -> false]].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) (not (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false])) -> false]]]; [(or (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) (not (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false])) -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 54, + "evals_used": 4633, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ['A -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal not_e@type and_el).", + "c x", + "=> (x iff_i@type or_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1961, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "c x", + "=> (x goal p2@type@2 and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e goal x1 and_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 332, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not false) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not false) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11938, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> x]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> x]].", + "c x0", + "=> (x0 not_i@type em@type not_i em).", + "c x0", + "=> (x0 and_i@type or_il@type x0 or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type em@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 iff_i@type or_il@type iff_i or_il).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c p8", + "=> (p8 exfalso@type and_i@type exfalso and_i).", + "c x1", + "=> (x1 and_i@type and_i@type p8 and_i).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso and_i).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em x2).", + "c x1", + "=> (x1 iff_er@type iff_i@type iff_er iff_i).", + "c x1", + "=> (x1 goal p11@type and_el p13).", + "c p8", + "=> (p8 p7@type and_i@type p7 p8).", + "c p8", + "=> (p8 p16@type p16@type p16 p16).", + "c x1", + "=> (x1 and_el@type p0@type and_el p0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 570, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)) (not (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and false (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ['P -> false] -> (not 'P)] (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))))))).", + "a or_e", + "=> [(and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> ('R : 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(and 'A 'B) -> 'B] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)) -> false]; [(not (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)) -> false]; [(not (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 547, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [false -> ('P : prop) 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em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal5).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em x0).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [x0 -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not x0) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [x0 -> [x0 -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not x0) -> [x0 -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p0@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x goal or_e@type and_er).", + "c x", + "=> (x iff_i@type or_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1962, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + 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false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 978, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)].", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> 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goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1328, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4455, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> 'B -> (and x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c and_el", + "=> (and_el exfalso@type or_ir@type p3).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x2", + "=> (x2 not_e@type p@type x0 p).", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_i@type or_il@type x2 or_il).", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a p4", + "=> false.", + "c em", + "=> (em goal1).", + "c x2", + "=> (x2 exfalso@type p2@type p4 p2).", + "c x2", + "=> (x2 iff_el@type p0@type iff_el p0).", + "a p4", + "=> false.", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_er@type em@type and_er em)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 545, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 499, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "c em", + "=> (em em@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "intro.", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "c em", + "=> (em exfalso@type).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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-> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))); (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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(and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])] (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 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-> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))]]]].", + "c x2", + "=> (x2 iff_er@type or_ir@type iff_er or_ir).", + "c x2", + "=> (x2 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+ "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "c x", + "=> (x or_il@type p3@type@2 or_il).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x", + "=> (x exfalso@type p6@type exfalso).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1521, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2243, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal14 x).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 364, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4579, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (or x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not x); x.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not x)].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p6@type p1 p6).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 536, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)])].", + "intro.", + "c x", + "=> (x goal not_i@type or_ir).", + "c x", + "=> (x iff_i@type or_ir@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2035, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal16 or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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: prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] [('P : prop) -> ['P -> false] -> (not 'P)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11938, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "c x0", + "=> (x0 not_i@type em@type not_i em).", + "c x0", + "=> (x0 and_i@type or_il@type x0 or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type em@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 iff_i@type or_il@type iff_i or_il).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c p8", + "=> (p8 exfalso@type and_i@type exfalso and_i).", + "c x1", + "=> (x1 and_i@type and_i@type p8 and_i).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso and_i).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em x2).", + "c x1", + "=> (x1 iff_er@type iff_i@type iff_er iff_i).", + "c x1", + "=> (x1 goal p11@type or_ir p13).", + "c p8", + "=> (p8 p7@type and_i@type p7 p8).", + "c p8", + "=> (p8 p16@type p16@type p16 p16).", + "c x1", + "=> (x1 and_el@type p0@type and_el p0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 1871, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 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-> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]]; [(not false) -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 529, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]; [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]; [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a or_e", + "=> [false -> [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]]; [(not false) -> [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false 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or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q 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'R] -> ['Q -> 'R] -> 'R] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] 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or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 663, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> ['B -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> ['B -> x]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + 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prop) -> (not 'A) -> 'A -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('A : prop) -> (not 'A) -> 'A -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 608, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not x) -> x -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not x) -> x -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('A : prop) -> (not 'A) -> 'A -> false]); [('A : prop) -> (not 'A) -> 'A -> false].", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a 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-> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type em@type not_e).", + "c x0", + "=> (x0 not_e@type p0@type not_e).", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [false -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) false); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [false -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q 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'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and x [false -> [false -> false]]).", + "a and_i", + "=> x; [false -> [false -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10964, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not x) -> x -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "c x0", + "=> (x0 not_e@type goal not_e not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c em", + "=> (em p1@type).", + "c x1", + "=> (x1 iff_i@type or_ir@type iff_i or_ir).", + "c and_el", + "=> (and_el not_e@type goal p3).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso x1).", + "c x1", + "=> (x1 exfalso@type not_i@type exfalso not_i).", + "c x0", + "=> (x0 and_i@type and_er@type x1 and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "c x1", + "=> (x1 or_ir@type p3@type or_ir p3).", + "a exfalso", + "=> false.", + "a p4", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x0", + "=> (x0 goal and_el@type x2 and_el).", + "c x1", + "=> (x1 p2@type p8@type p2 p8).", + "c x1", + "=> (x1 p13@type p11@type p13 p11).", + "c x0", + "=> (x0 and_er@type p2@type and_er p2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4848, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not 'A) -> 'A -> false]); [('A : prop) -> (not 'A) -> 'A -> false].", + "a not_i", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type).", + "intro.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not (not (not [('A : prop) -> (not 'A) -> 'A -> false]))); (not (not [('A : prop) -> (not 'A) -> 'A -> false])).", + "a x0", + "=> (or [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] [false -> ('P : prop) -> 'P]); [[(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] -> (not (not (not [('A : prop) -> (not 'A) -> 'A -> false])))]; [[false -> ('P : prop) -> 'P] -> (not (not (not [('A : prop) -> (not 'A) -> 'A -> false])))].", + "a or_ir", + "=> .", + "a x0", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); [(not [('P : prop) -> (or 'P (not 'P))]) -> [[(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] -> (not (not (not [('A : prop) -> (not 'A) -> 'A -> false])))]]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] -> (not (not (not [('A : prop) -> (not 'A) -> 'A -> false])))]].", + "c em", + "=> (em and_el@type).", + "a x0", + "=> (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (or (not [('P : prop) -> (or 'P (not 'P))]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [[false -> ('P : prop) -> 'P] -> (or (not [('P : prop) -> (or 'P (not 'P))]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('A : prop) -> (not 'A) -> 'A -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> 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: prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [(or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])) -> false] (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])) -> false] (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p0@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]); [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + 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-> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9747, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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(and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])])))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])])))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (and false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (or x0 (not x0)))).", + "a x1", + "=> (and (and false (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]])] (or x0 (not x0)))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('A : prop) -> (or 'A (not 'A))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x goal not_i@type em).", + "c x", + "=> (x iff_i@type not_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('A : prop) -> (or 'A (not 'A))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('A : prop) -> (or 'A (not 'A))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> (or 'A (not 'A))]); [('A : prop) -> (or 'A (not 'A))].", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> (not [('A : prop) -> (or 'A (not 'A))])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('A : prop) -> (or 'A (not 'A))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7720, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (or 'A (not 'A))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (or 'A (not 'A))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p0@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "a x", + "=> (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]]); [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 446, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em em@type).", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> 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'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p4@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ['A -> false] -> (not 'A)] -> false]; [(not [('A : prop) -> ['A -> false] -> (not 'A)]) -> false].", + "a x", + "=> (and [[('A : prop) -> ['A -> false] -> (not 'A)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a and_i", + "=> [[('A : prop) -> ['A -> false] -> (not 'A)] -> false].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [false -> ('P : prop) -> 'P]) -> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1457, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x goal not_i@type not_i).", + "c x", + "=> (x iff_i@type or_ir@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ['A -> false] -> (not 'A)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1994, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x goal goal16 not_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]; [false 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-> 'Q -> (or 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C])]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]); [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c em", + "=> (em goal4).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]))); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C])) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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(and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] 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prop) -> 'P -> (or 'P 'Q)])]; [[[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 458, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) 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['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> (or 'P (not 'P))])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a x0", + "=> (or (or [('P : prop) -> 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_ir" + ] + } + ], + "problem": "extrinsic_L0_14" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 27112, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> 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-> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('A : prop) -> 'A -> (not (not 'A))]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> 'A -> (not (not 'A))] -> false]; [(not [('A : prop) -> 'A -> (not (not 'A))]) -> false].", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em goal8).", + "a x", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> 'A -> (not (not 'A))] (not [('A : prop) -> 'A -> (not (not 'A))]))).", + "a or_e", + "=> [[('A : prop) -> 'A -> (not (not 'A))] -> (not (or [('A : prop) -> 'A -> (not (not 'A))] (not [('A : prop) -> 'A -> (not (not 'A))])))]; [(not [('A : prop) -> 'A -> (not (not 'A))]) -> (not (or [('A : prop) -> 'A -> (not (not 'A))] (not [('A : prop) -> 'A -> (not (not 'A))])))].", + "a or_e", + "=> [[[('A : prop) -> 'A -> (not (not 'A))] -> false] -> [[('A : prop) -> 'A -> (not (not 'A))] -> (not (or [('A : prop) -> 'A -> (not (not 'A))] (not [('A : prop) -> 'A -> (not (not 'A))])))]]; [(not [[('A : prop) -> 'A -> (not (not 'A))] -> false]) -> [[('A : prop) -> 'A -> (not (not 'A))] -> (not (or [('A : prop) -> 'A -> (not (not 'A))] (not [('A : prop) -> 'A -> (not (not 'A))])))]].", + "a or_e", + "=> [[[('A : prop) -> 'A -> (not (not 'A))] -> false] -> [[[('A : prop) -> 'A -> (not (not 'A))] -> false] -> [[('A : prop) -> 'A -> (not (not 'A))] -> (not (or [('A : prop) -> 'A -> (not (not 'A))] (not [('A : prop) -> 'A -> (not (not 'A))])))]]]; [(not [[('A : prop) -> 'A -> (not (not 'A))] -> false]) -> [[[('A : prop) -> 'A -> (not (not 'A))] -> false] -> [[('A : prop) -> 'A -> (not (not 'A))] -> (not (or [('A : prop) -> 'A -> (not (not 'A))] (not [('A : prop) -> 'A -> (not (not 'A))])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em goal19).", + "a x1", + "=> [('A : prop) -> 'A -> (not (not 'A))].", + "a x", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : 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-> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "a x", + "=> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a and_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] 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(or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7864, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> 'A -> (not (not 'A))]]; [(not 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false]; [[false -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> false])]].", + 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not false) -> [[false -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a or_il", + "=> (not false).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or (not false) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not false)]; [(or (not false) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not false)].", + "a x", + "=> (or (not [false -> false]) (or (not false) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [false -> false]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or (not false) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(or (not false) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or (not false) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 361, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 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prop) -> 'P]))) -> false].", + "intro.", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em not_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2848, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> 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-> false] -> (not 'P)] -> false]].", + "c p7", + "=> (p7 goal10 and_i@type x0).", + "c em", + "=> (em goal18).", + "c p7", + "=> (p7 p4@type p6@type p6)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 766, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : 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-> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p5@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3867, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : 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-> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_il", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c em", + "=> (em or_ir@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1994, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + 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x1", + "=> (x1 goal10).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]].", + "c x2", + "=> (x2 em@type exfalso@type x1 exfalso).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p2@type or_e@type p2 or_e).", + "c x1", + "=> (x1 goal19).", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1185, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c x", + "=> (x iff_i@type em@type iff_i em).", + "c and_er", + "=> (and_er iff_i@type em@type p1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c p2", + "=> (p2 goal13).", + "c and_el", + "=> (and_el iff_i@type em@type p1).", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not false)].", + "c x", + "=> (x or_il@type p@type or_il p).", + "intro.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el or_il@type p@type p7).", + "c x0", + "=> (x0 em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 7513, + "actions": [ + 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(not 'P))])))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and false (and false [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> (or 'P (not 'P))]) (and (and (and false (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and false (and false [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and false (and false [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> (or 'P (not 'P))]) (and (and (and false (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and false (and false [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]])) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 325, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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+ "=> (em goal8).", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em p8@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p5@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "intro.", + "c em", + "=> (em p6@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2348, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p6@type@2 and_er@type and_er).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x1", + "=> (x1 goal not_e@type not_e).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6870, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]].", + "a x2", + "=> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]].", + "a x2", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) -> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a x2", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x0); [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [x0 -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "c x1", + "=> (x1 p1@type p1@type p1).", + "a x1", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1467, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c p5", + "=> (p5 or_ir).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2137, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1329, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or false (not false))); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + "evals_used": 6418, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "c x0", + "=> (x0 not_i@type or_e@type not_i or_e).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_e@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 iff_el@type p15@type iff_el p15).", + "c x1" + ] + } + ], + "problem": "extrinsic_L1_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 33949, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p2@type).", + "c x1", + "=> (x1 goal10).", + "a exfalso" + ] + }, + { + "mode": "sample", 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prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1857, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e or_e@type x1 x0).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "c x0", + "=> (x0 not_i@type or_il@type not_i or_il).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_il@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 593, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 goal10).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]); [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])].", + "intro.", + "c not_e", + "=> (not_e or_ir@type x1 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 514, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c em", + "=> (em p0@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a x1", + "=> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "intro.", + "a x0", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]).", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (and [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))])).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 423, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]))).", + "a or_e", + "=> [false -> (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))]; [(not false) -> (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))].", + "a or_e", + "=> [false -> [false -> (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))]]; [(not false) -> [false -> (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))]].", + "intro.", + "intro.", + "a exfalso", + "=> .", + "intro.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not false) -> (not (or 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"evals_used": 545, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])) -> false].", + "intro.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)].", + "c em", + "=> (em p0@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> false].", + "c em", + "=> (em goal4).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])); (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]]; [(not (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]))); (not (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])).", + "c em", + "=> (em p2@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 387, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x and_el@type p@type@2 p).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x not_e@type p6@type@2 p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + 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em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2118, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff false false)); (iff false false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (iff false false))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (iff false false))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (iff false false))).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (iff false false)))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (iff false false)))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "c x0", + "=> (x0 not_i@type or_il@type not_i or_il).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_il@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2491, + 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or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro.", + "c not_e", + "=> (not_e or_ir@type x2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 51, + "evals_used": 6535, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A 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'P -> 'Q -> (and 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_ir", + "=> .", + "intro.", + "a x0", + "=> (iff (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (iff (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[false -> ('P : prop) -> 'P] -> (iff (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_ir" + ] + } + ], + "problem": "extrinsic_L2_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 29357, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) 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-> 'B] -> [['B -> 'C] -> ['A -> 'C]]])))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x p1@type iff_el@type p1 iff_el).", + "c and_er", + "=> (and_er p1@type iff_el@type p6).", + "c and_el", + "=> (and_el p1@type iff_el@type p6).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x", + "=> 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 950, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(not [('P : prop) -> 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]].", + "c x2", + "=> (x2 em@type exfalso@type x1 exfalso).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p2@type or_e@type p2 or_e).", + "c x1", + "=> (x1 goal19).", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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"a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5584, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[false -> false] -> false]; [(not [false -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[false -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x0", + "=> .", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> (not 'P) -> 'P -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> false] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> false] -> false]]].", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + 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not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1054, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c x4", + "=> (x4 goal19 or_ir@type or_ir).", + "intro.", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 621, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) 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prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))])))) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 680, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em 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false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> (or 'P (not 'P))]); [false -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]].", + "a or_il", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c 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-> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a not_i", + "=> [(not false) -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]] (not (not false))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]] -> [(not false) -> false]]; [(not (not false)) -> [(not false) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]); [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (not false) [false -> [false -> false]]).", + "a and_i", + "=> (not false); [false -> [false -> false]].", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4270, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 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'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> 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: prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> 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false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (not [false -> ('P : prop) -> 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-> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 481, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x x)].", + "intro.", + "c and_er", + "=> (and_er x x x0).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : 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false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)].", + "c em", + "=> (em goal0@1).", + "c x3", + "=> (x3 p5@type).", + "intro.", + "a iff_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [false -> [('P : prop) -> ['P -> false] -> (not 'P)]].", + "intro.", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x5", + "=> [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 428, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [false -> ('P : prop) -> 'P]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "intro.", + "intro.", + "a iff_i", + "=> [(and x0 x0) -> x0]; [x0 -> (and x0 x0)].", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(and x0 x0) -> x0]); [(and x0 x0) -> x0].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [(and 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prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "a x1", + "=> false.", + "a x1", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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-> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not (or 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[(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]); [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 720, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [(and x false) -> 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('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "c em", + "=> (em not_e@type).", + "c and_er", + "=> (and_er x false x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "c em", + "=> (em p2@type).", + "intro.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "intro.", + "c x2", + "=> (x2 x false x0).", + "c em", + "=> (em p4@type@2).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))].", + "intro.", + "c x3", + "=> (x3 x false x0).", + "a x1", + "=> (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))).", + "a x2", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))).", + "a x2", + "=> (and (iff (and x false) false) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))))).", + "a x1", + "=> (and (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) (and (iff (and x false) false) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))))).", + "a and_i", + "=> (and (iff (and x false) false) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))))).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> (and (iff (and x false) false) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))))]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> (and (iff (and x false) false) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))))].", + "a x1", + "=> (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) [[('A : prop) -> (iff (and 'A false) false)] -> (and (iff (and x false) false) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('A : prop) -> (iff (and 'A false) false)]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5337, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (iff (and x false) false)); (iff (and x false) false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "c x0", + "=> (x0 p6@type p1@type@2 p6).", + "c x0", + "=> (x0 exfalso@type p3@type@2 exfalso).", + "c x0", + "=> (x0 p8@type x p8).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 iff_el@type p6@type@2 iff_el).", + "c x0", + "=> (x0 p3@type exfalso@type p3).", + "a not_e", + "=> (not (or (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p7@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6783, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [(and x false) -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [(and x false) -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]].", + "intro.", + "c em", + "=> (em false).", + "intro.", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(or [('P : prop) -> ('Q 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false]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 476, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c em", + "=> (em p0@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false].", + "c em", + "=> (em goal1).", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('A : prop) -> (iff (and 'A false) false)]); [('A : prop) -> (iff (and 'A false) false)].", + "c em", + "=> (em goal11).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 427, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 false p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x p@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 50, + "evals_used": 1318, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L2_9" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19538, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + 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: prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not false) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] (not [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "dead", + "depth_used": 42, + "evals_used": 1133, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]); [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false].", + "intro.", + "c x", + "=> (x or_e@type and_el@type or_e).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x", + "=> (x not_i@type exfalso@type not_i).", + "c x", + "=> (x exfalso@type false exfalso).", + "c iff_el", + "=> (iff_el exfalso@type p0@type@2 p0).", + "c p2", + "=> (p2 exfalso).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c iff_er", + "=> (iff_er false p1@type@2 p1).", + "a p5", + "=> (and [false -> ('P : prop) -> 'P] false).", + "c iff_er", + "=> (iff_er exfalso@type p0@type@2 p0).", + "c p6", + "=> (p6 p3).", + "c p2", + "=> (p2 p7).", + "a p7", + "=> false.", + "a p7", + "=> false.", + "a p5", + "=> (and [false -> ('P : prop) -> 'P] false).", + "c and_er" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 487, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "intro.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> [(not false) -> false]]; [(not false) -> [(not false) -> false]].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [false -> [false -> [(not false) -> false]]]; [(not false) -> [false -> [(not false) -> false]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [false -> [(not false) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [false -> [(not false) -> false]]].", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [false -> [(not false) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [false -> [(not false) -> false]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p0@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false." + ] + }, + { + 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-> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]]].", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c not_e", + "=> (not_e exfalso@type x exfalso).", + "c em", + "=> (em goal14).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 280, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> false]; [(not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> false].", + "intro.", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "c x0", + "=> (x0 exfalso).", + "c x0", + "=> (x0 x).", + "a exfalso", + "=> false.", + "a x", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1208, + "actions": [ + "c em", + 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'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 iff_i).", + "c iff_er", + "=> (iff_er em@type p5@type@2 p5).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c p6", + "=> (p6 em).", + "c x", + "=> (x em@type p5@type@2 p6 p8).", + "c em", + "=> (em false).", + "c x0", + "=> (x0 x).", + "c x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 513, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]); [('A : prop) -> ('B : prop) -> 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-> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em iff_i@type).", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x", + "=> (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x0", + "=> (and (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3404, + "actions": [ + "intro.", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (not x)); (not x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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: prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 429, + "actions": [ + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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-> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal1).", + "intro.", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]]) -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 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prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a x", + "=> (and (and [('P : prop) -> ['P -> false] -> (not 'P)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]])) false).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and (and [('P : prop) -> ['P -> false] -> (not 'P)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]])) false)).", + "a x0", + "=> (and false (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and (and [('P : prop) -> ['P -> false] -> (not 'P)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]])) false))).", + "a x", + "=> (and [false -> ('P : prop) -> 'P] (and false (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and (and [('P : prop) -> ['P -> false] -> (not 'P)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]])) false))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 607, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]]; [(not [('P : prop) -> 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em iff_er@type).", + "intro.", + "c em", + "=> (em p7@type).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false).", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)].", + "a x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5594, + "actions": [ + "intro.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em goal).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (iff x0 (and x x0))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> (iff x0 (and x x0))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (iff x0 (and x x0))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (iff x0 (and x x0))]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B 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prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]]]].", + "c em", + "=> (em iff_er@type).", + "intro.", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]]]].", + "a exfalso", + "=> false.", + "a x1", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]); [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a x1", + "=> (or (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a x1", + "=> (or x [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [x -> (or (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or x [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or x [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 487, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e or_e@type x or_e).", + "c em", + "=> (em 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal8).", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 419, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e not_i@type x not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e" + ] + } + ], + "problem": "extrinsic_L2_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 28861, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 374, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [x -> x]; [x -> x].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> x]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [x -> x]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 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(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]; [(not (not [x0 -> x0])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [x0 -> x0]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [(not [x0 -> x0]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x", + "=> (x and_el@type x3 and_el).", + "c em", + "=> (em p5@type).", + "c x1", + "=> (x1 and_el@type x3 and_el).", + "c x2", + "=> (x2 and_el@type x3 and_el).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('A : prop) -> (iff 'A 'A)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('A : prop) -> (iff 'A 'A)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff 'A 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]]].", + "a x", + "=> (or (not false) false); [(not false) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [false -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 306, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a iff_i", + "=> [x -> x]; [x -> x].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : 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-> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8601, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c x0", + "=> (x0 or_ir@type or_ir@type or_ir or_ir).", + "c and_el", + "=> (and_el or_ir@type or_ir@type p1).", + "a exfalso", + "=> false.", + "c and_er", + "=> (and_er or_ir@type or_ir@type p1).", + "c p2", + "=> (p2 goal7 and_i@type and_i).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c p2", + "=> (p2 x not_i@type not_i).", + "c and_er", + "=> (and_er and_er@type or_il@type p5).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em p4@type).", + "intro.", + "c p2", + "=> (p2 em@type p6@type p6).", + "c x0", + "=> (x0 p9@type and_i@type p9 and_i).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c x0", + "=> (x0 iff_i@type or_il@type iff_i p7).", + "c p7", + "=> (p7 p1@type x p1).", + "c p7", + "=> (p7 p12@type not_e@type p12).", + "c p2", + "=> (p2 or_ir@type and_i@type and_i).", + "c and_el", + "=> (and_el p9@type and_i@type p11).", + "c and_er", + "=> (and_er p9@type and_i@type p11)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 54, + "evals_used": 6570, + "actions": [ + "intro.", + "c em", + "=> (em 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "a x0", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type).", + "intro.", + "c em", + "=> (em x).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff 'A 'A)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [[('A : prop) -> (iff 'A 'A)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_il", + "=> .", + "a x0", + "=> [[('A : prop) -> (iff 'A 'A)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('A : prop) -> (iff 'A 'A)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a x0", + "=> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [false -> [[('A : prop) -> (iff 'A 'A)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('A : prop) -> (iff 'A 'A)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('A : prop) -> (iff 'A 'A)])); [[('P : prop) -> (or 'P (not 'P))] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('A : prop) -> (iff 'A 'A)]) -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_ir", + "=> (not [('A : prop) -> (iff 'A 'A)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : 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p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or [('P : prop) -> (or 'P (not 'P))] false); [[('P : prop) -> (or 'P (not 'P))] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]])]; [false -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> (or 'P (not 'P))] false)]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> (or 'P (not 'P))] false)].", + "a p4", + "=> (or (or [('P : prop) -> (or 'P (not 'P))] false) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [(or [('P : prop) -> (or 'P (not 'P))] false) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]))); [(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 370, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + 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prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]); [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]].", + "a exfalso", + "=> false.", + "a x2", + "=> false.", + "a x3", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [[false -> ('P : prop) -> 'P] -> false])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [[false -> ('P : prop) -> 'P] -> false]))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [[false -> ('P : prop) -> 'P] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)].", + "c em", + 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'B) -> (iff 'B 'C) -> (iff 'A 'C)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : 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'P])) -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]))) -> (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not [('P : prop) -> ['P -> false] -> (not 'P)]))]." + ] + }, + { + "mode": 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : 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-> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em 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-> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 618, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal7).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 55, + "evals_used": 2589, + 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[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])].", + "c x1", + "=> (x1 iff_i@type not_e@type x).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 goal9 not_e@type x).", + "a or_e", + "=> [(not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]); [(not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]) -> (not 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('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))])]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x1", + "=> (x1 p4@type or_ir@type x1).", + "c em", + "=> (em p5@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 or_ir).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "a exfalso", + "=> false.", + "c em", + 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(not 'A)]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]); [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2078, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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-> [false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] -> false]; [(not [false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] -> false]].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not false) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] -> false]]]; [(not (not false)) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 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-> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not x0); x0.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not x0)]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> (not x0)].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x or_ir@type p3 or_ir).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6972, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [false -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]))); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]))) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]))) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 370, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])); (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9118, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3466, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + 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'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x0", + "=> (x0 p4@type@2 and_el@type and_el).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 p1@type and_i@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p0@type or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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and_er", + "=> (and_er p0@type not_e@type p3).", + "a not_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c x", + "=> (x not_e@type iff_el@type not_e iff_el).", + "c x", + "=> (x iff_el@type em@type iff_el em).", + "c and_er", + "=> (and_er not_e@type iff_el@type p6).", + "c x", + "=> (x em@type iff_i@type em iff_i).", + "c and_el", + "=> (and_el not_e@type iff_el@type p6).", + "c and_el", + "=> (and_el em@type iff_i@type p9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c p11", + "=> (p11 not_i@type).", + "intro.", + "c and_el", + "=> (and_el iff_el@type em@type p7).", + "intro.", + "a p5", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c p11" + ] + }, + { + "mode": 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+ "c em", + "=> (em p0@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not false) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not false) -> false]; [(not (not false)) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> 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false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6404, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> 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['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]] [('P : prop) -> (or 'P (not 'P))]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 631, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "c em", + "=> 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"intro.", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "a or_e", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]]; [(not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]].", + "intro.", + "c em", + "=> (em goal19).", + "c x", + "=> (x goal10 x3 x4).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 goal10 x3 x4).", + "c x2", + "=> (x2 goal10 x3 x4).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> false].", + "a x0", + "=> (and [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em 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-> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 not_i@type or_il@type or_il).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x0", + "=> (x0 p4@type@2 and_el@type and_el).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x1", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p0@type or_e@type or_e).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2631, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> 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-> (or 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]] false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]] false))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 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(and (not 'A) (not 'B)) -> (not (or 'A 'B))]))].", + "c em", + "=> (em p@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])].", + "a x", + "=> (or (not (or [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]))) [('P : prop) -> (or 'P (not 'P))]); [(not (or [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]))) -> (or [('P : prop) 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-> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> false])]]; [(not [('P : 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "c x1", + "=> (x1 or_e@type iff_i@type or_e iff_i).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type iff_i@type p1).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false].", + "a p4", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]] -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]])))); [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]])]; [(or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]))) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]])].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]))))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]) (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]))))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))])); (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1855, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type and_el@type and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 1445, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a 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(not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> (or 'P (not 'P))]))); (not (not [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (not [('P : prop) -> (or 'P (not 'P))])))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> (or 'P (not 'P))])))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> (or 'P (not 'P))])))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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: prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + 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-> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ['P -> false] -> (not 'P)])); [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a 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or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 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60, + "evals_used": 444, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "intro.", + "c em", + "=> (em p0@type@2).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 680, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c 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-> [(not 'B) -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + 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[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]]))).", + "c x3", + "=> (x3 x1).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 406, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 677, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]].", + "a or_e", + "=> [false -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]; [(not false) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a x1", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em x2).", + "c em", + "=> (em goal13).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1686, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_ir@type or_ir).", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]); [[('P : 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 442, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> [x -> false]]]]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "a x0", + "=> (iff [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> [x -> false]]]]]).", + "a iff_i", + "=> [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> [x -> false]]]]]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> [x -> false]]]]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "c x5", + "=> (x5 x1).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 559, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff (not 'A) ['A -> false])]].", + "intro.", + "intro.", + "a iff_i", + "=> [(not x0) -> [x0 -> false]]; [[x0 -> false] -> (not x0)].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x0) -> [x0 -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not x0) -> [x0 -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not x0); x0.", + "a not_i", + "=> [x0 -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x0 -> false]].", + "intro.", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [x0 -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [x0 -> false]].", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal9).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [(not x0) -> [x0 -> false]] (not [(not x0) -> [x0 -> false]]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff (not x0) [x0 -> false])); (iff (not x0) [x0 -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (iff (not x0) [x0 -> false]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (iff (not x0) [x0 -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (iff (not x0) [x0 -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (iff (not x0) [x0 -> false]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (iff (not x0) [x0 -> false]))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (iff (not x0) [x0 -> false]))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x3", + "=> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [x0 -> false]]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1466, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (not 'A) ['A -> false])]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a not_e", + 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false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 351, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2258, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x0", + "=> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) false).", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7706, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "a exfalso", + "=> false.", + "c em", + "=> 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['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a x0", + "=> (or (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 362, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P 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false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : 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-> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em false).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a or_e", + "=> [false -> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not false) -> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not 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prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) 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'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> (not (not (not 'A))) -> (not 'A)] (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]))).", + "a or_e", + "=> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> (not (or [('A : prop) -> (not (not (not 'A))) -> (not 'A)] (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)])))]; [(not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]) -> (not (or [('A : prop) -> 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false]; (not (or [('A : prop) -> (not (not (not 'A))) -> (not 'A)] (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]))).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ 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prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]; [(or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P]))]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1389, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or x [('P : prop) -> ['P -> false] -> (not 'P)]); [x -> [false -> [false -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [false -> false]]].", + "a or_il", + "=> x.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + 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prop) -> 'P])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not (not [false -> ('P : prop) -> 'P])) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "intro.", + "c not_e", + "=> (not_e exfalso@type x2 exfalso).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "intro.", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "intro.", + "c em", + "=> (em goal17).", + "c x", + "=> (x goal10 x2 x3).", + "c em", + "=> (em p2@type).", + "c x", + "=> (x exfalso@type x3 exfalso).", + "c x1", + "=> (x1 goal10 x2 x3).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> false] -> false]; [(not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> false]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> false] -> false]; [(not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> false]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6796, + "actions": [ + "c em", + "=> 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: prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])); [(or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (and [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(and [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(and [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(and [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 527, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "intro.", + "c x1", + "=> (x1 x0).", + "intro.", + "a not_e", + 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"a exfalso", + "=> false.", + "c x", + "=> (x p0@type iff_el@type p0).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c x", + "=> (x exfalso@type p1@type@2 exfalso).", + "c x", + "=> (x em@type not_i@type em).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type goal1 p0).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [false -> ('P : prop) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso", + "=> false.", + "c x", + "=> (x or_ir@type p2@type or_ir).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> 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-> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x3", + "=> (x3 iff_el@type exfalso@type iff_el exfalso).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2138, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [false -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not false)); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 47, + "evals_used": 4431, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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-> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])]; [(not false) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])].", + "a or_e", + "=> [false -> [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])]]; [(not false) -> [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 621, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not 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-> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false])); (not [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false]))]; 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false])])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x2", + "=> false.", + "a x3", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 413, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) 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-> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : 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prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (not 'P) -> 'P -> false]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 593, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(iff x (not x)) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(iff x (not x)) -> false]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "c em", + "=> (em not_i@type).", + "c iff_er", + "=> (iff_er x x2@type@2 x2).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : 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(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]].", + "intro.", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> .", + "c em", + "=> (em goal1).", + "c em", + "=> (em x2@type@2).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p9@type).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2483, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "c em", + "=> (em goal).", + "a x", + "=> (iff (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a iff_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 459, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + 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(not 'P))]))) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x0", + "=> (and (and false (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and (and false (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and (and false (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2359, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "a or_e", + "=> [(or false (not false)) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or false (not false)) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or false (not false)) -> false]].", + "c x1", + "=> (x1 not_e@type or_il@type not_e).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 442, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]; [(not 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x1", + "=> (x1 and_i).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 307, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]] -> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 5339, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em" + ] + } + ], + "problem": "extrinsic_L3_26" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 22169, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + 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+ "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 416, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))].", + "c em", + "=> (em goal10).", + "a or_e", + "=> [(not (not [false -> ('P : prop) -> 'P])) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))])]; [(not (not (not [false -> ('P : prop) -> 'P]))) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))])].", + "intro.", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))] -> false].", + "intro.", + "c x3", + "=> (x3 not_e).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x3", + "=> (x3 x).", + "c x3", + "=> (x3 x1).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (not (not [false -> ('P : prop) -> 'P])) (not (not (not [false -> ('P : prop) -> 'P]))))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal6).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> 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x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2137, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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-> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]); [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (not (not 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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not_i", + "=> [(or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] 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false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 9440, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em 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and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 x p3@type p3).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir p9).", + "c x1", + "=> (x1 not_i@type p5@type p6 p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false p@type p).", + "c x1", + "=> (x1 iff_el@type and_i@type iff_el and_i).", + "c and_er", + "=> (and_er iff_el@type and_i@type p14).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 p10@type iff_i@type p10 iff_i).", + "c em", + "=> (em p8@type).", + "c em", + "=> (em p17@type@2).", + "c x1", + "=> (x1 p14@type p16@type p14 p16)." + ] + } + ], + 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x2", + "=> (and [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])]] (iff x0 (not (not x0)))).", + "c em", + "=> (em goal22).", + "c x3", + "=> (x3 x1).", + "c p6", + "=> (p6 goal10).", + "c iff_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 424, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> (iff 'A (not (not 'A)))] (not [('A : prop) -> (iff 'A (not (not 'A)))]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('A : prop) -> (iff 'A (not (not 'A)))] (not [('A : prop) -> (iff 'A (not (not 'A)))])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('A : prop) -> (iff 'A (not (not 'A)))] (not [('A : prop) -> (iff 'A (not (not 'A)))])))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not (not 'A)))] -> false]; [(not [('A : prop) -> (iff 'A (not (not 'A)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not (not 'A)))] -> false]; [(not [('A : prop) -> (iff 'A (not (not 'A)))]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c iff_er", + "=> (iff_er not_i@type p5@type@2 p5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('A : prop) -> 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(or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not 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-> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]] -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [x -> (not (not x))]; [(not (not x)) -> x].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 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+ "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10466, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_il", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ['P -> 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-> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> (not 'P) -> 'P -> false])]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ['P -> false] -> (not 'P)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 541, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : 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-> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 637, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not false)); (not false).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2485, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_il@type or_il).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]); [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 p4@type@2 and_el@type 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal6).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_ir", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0); x0.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not x0)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x1", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]])) [[false -> ('P : prop) -> 'P] -> false]); [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]]; [[[false -> ('P : prop) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]].", + "c em", + "=> (em goal21).", + "a x1", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]])) [[false -> ('P : prop) -> 'P] -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]])) [[false -> ('P : prop) -> 'P] -> false])].", + "c x3", + "=> (x3 iff_el@type iff_i@type iff_el iff_i).", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 286, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false].", + "a x", + "=> [(not false) -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false].", + "a x", + "=> [(not false) -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not false) -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not false) -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 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false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "c em", + "=> (em p3@type@2).", + "c x0", + "=> (x0 and_er@type).", + "c x0", + "=> (x0 or_il@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 527, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : 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(or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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prop) -> 'P -> (or 'P 'Q)])); [false -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [(or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1329, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9118, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> 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false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x1", + "=> (x1 iff_i@type not_i@type x0 not_i).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 677, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]].", + "a exfalso", + "=> 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-> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em and_el@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7276, + "actions": [ + "intro.", + "a exfalso", + 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exfalso", + "=> false.", + "a x2", + "=> (or (not [false -> ('P : prop) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(not [false -> ('P : prop) -> 'P]) -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "c x0", + "=> (x0 p6@type false p6).", + "a x2", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> (or (not [false -> ('P : prop) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) -> (or (not [false -> ('P : prop) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> 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-> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]].", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not false)); (not false)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 431, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + 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false].", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", 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x0", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p6@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2079, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 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[false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3872, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]].", + "c x2", + "=> (x2 em@type and_i@type em and_i).", + "c x2", + "=> (x2 iff_i@type iff_el@type iff_i iff_el).", + "c x2", + "=> (x2 p2@type or_ir@type p2 or_ir).", + "c x1", + "=> (x1 p4@type em@type p4).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 402, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7331, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [false -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]; [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]]; [(or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]].", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 371, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]])))).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + } + ], + "problem": "extrinsic_L4_8" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 39896, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 401, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> false]; [(not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] (not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]))).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> (not (or [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] (not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])))]; [(not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> (not (or [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] (not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (or [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] (not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] (not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])))].", + "intro.", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] (not [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10433, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c x", + "=> (x or_ir@type and_er@type or_ir).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x", + "=> (x or_e@type iff_el@type or_e).", + "c x", + "=> (x not_e@type and_i@type not_e).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type and_el@type p1).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p@type).", + "c x", + "=> (x and_er@type not_i@type and_er).", + "c em", + "=> (em p4@type).", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "c x", + "=> (x p7@type p@type p7).", + "c x", + "=> (x or_il@type exfalso@type or_il).", + "c x", + "=> (x p7@type not_i@type p7).", + "c x", + "=> (x iff_er@type p@type iff_er).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c x", + "=> (x not_i@type not_e@type not_i).", + "a exfalso", + "=> false.", + "c x", + "=> (x and_el@type or_ir@type and_el).", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type or_ir@type and_er).", + "c x", + "=> (x and_er@type iff_el@type and_er)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "a x0", + "=> (iff [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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(not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_i@type and_el@type x0 and_el).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 477, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1870, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8695, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]].", + "c x0", + "=> (x0 not_i@type or_e@type not_i or_e).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_e@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er 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false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))))].", + "intro.", + "c not_e", + "=> (not_e or_e@type x1 or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 674, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]]].", + "c em", + "=> (em not_e@type).", + 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-> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]).", + "a x", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> [['A -> 'B] -> 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prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] false)))]).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 424, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c 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x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]; [(or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> (or [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : 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['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + 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(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]); [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", 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false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type).", + "intro.", + "c em", + "=> (em goal).", + "a not_e" + ] + } + ], + "problem": "extrinsic_L4_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 21127, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 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false]).", + "a or_e", + "=> [(or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]; [(not (or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 420, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 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(or 'P 'Q)])].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p1@type@2).", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a and_i", + "=> [[('P : 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-> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]] -> false]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [('P : prop) -> ['P -> false] -> (not 'P)]] -> false].", + "c x", + "=> (x p@type@2 p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", 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+ "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + 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'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [false -> [false -> false]]].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9315, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or [x -> 'B] ['B -> x])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or [x -> 'B] ['B -> x])]].", + "c x0", + "=> (x0 not_i@type or_il@type not_i or_il).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_il@type p1).", + "c em", + "=> (em goal4).", 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false.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type).", + "intro.", + "c em", + "=> (em p@type@2).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 iff_i@type p4@type p4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 iff_i@type exfalso@type exfalso).", + "a x", + "=> (iff (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 p3@type@2 iff_i@type iff_i).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (iff (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em p@type).", + "a x", + "=> (iff (iff (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 640, + "actions": [ + "intro.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; 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-> 'R] -> ['Q -> 'R] -> 'R] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(or [false -> ('P : prop) -> 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] (and [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]] (and [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]] false)))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] (and [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]] (and [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] 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['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2132, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4269, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 536, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])].", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])] -> false].", + "intro.", + "c x1", + "=> (x1 p2).", + "a not_e", + "=> (not (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))); (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 goal7).", + "a not_i", + "=> [(not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 650, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> 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'A 'B))] -> (and (and (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and (and false [('P : prop) -> (or 'P (not 'P))]) [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])) (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [false -> ('P : prop) -> 'P])) (and (and (and false [('P : prop) -> (or 'P (not 'P))]) [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))] (and (and false [('P : prop) -> (or 'P (not 'P))]) [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]))).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false.", + "a or_e", + "=> [(and false [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (and false [('P : prop) -> (or 'P (not 'P))])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and false [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (and false [('P : prop) -> (or 'P (not 'P))])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x0", + "=> (x0 iff_er).", + "c p7", + "=> (p7 p@type@2).", + "c p7", + "=> (p7 p8@type@2).", + "c iff_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4493, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a 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(x0 iff_el@type iff_el@type iff_el).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]]]; [(or (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]]].", + "intro.", + "c x0", + "=> (x0 p0@type p2@type p0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + 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-> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> 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-> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 364, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 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false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 655, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and 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prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a or_il", + "=> .", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]].", + "c em", + "=> (em and_el@type).", + "a x0", + "=> (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P 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prop) -> (or 'P (not 'P))] -> false]]]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type iff_el@type p0).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : 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false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 423, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a 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+ "=> false.", + "c x0", + "=> (x0 goal4 and_el@type and_el)." + ] + } + ], + "problem": "extrinsic_L5_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19103, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 182, + "actions": [ + "c em", + "=> (em false).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": 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('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4271, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 548, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 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'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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-> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + 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['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : 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-> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] false); [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> false]]]; [false -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4273, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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['A -> 'B]) (and 'A (not 'B)))]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]].", + "a x1", + "=> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false])); [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal9).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]) -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]]].", + "c x3", + "=> (x3 x2).", + "c x3", + "=> (x3 iff_er).", + "a x2", + "=> (iff [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 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x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2081, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : 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+ "c em", + "=> (em goal13).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 490, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c not_e", + "=> (not_e not_e@type x0 not_e).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em p3@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 475, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))].", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5716, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal6).", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "a or_ir", + "=> .", + "intro.", + "c not_e", + "=> (not_e or_e@type x2 or_e).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "intro.", + "intro.", + "c not_e", + "=> (not_e or_e@type x2 x1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "c x4", + "=> (x4 iff_er@type and_el@type iff_er and_el).", + "c x4", + "=> (x4 exfalso@type or_e@type exfalso or_e).", + "c x4", + "=> (x4 p0@type goal3 p0 x2).", + "a x1", + "=> (or [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]].", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3137, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x not_i@type iff_er@type).", + "intro.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> false].", + "c x", + "=> (x p@type@2 p5@type).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] false); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] false)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] false)]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] false)]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) [('P : prop) -> (not 'P) -> 'P -> false]); [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10529, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em goal4@2).", + "c x1", + "=> (x1 exfalso@type and_er@type exfalso and_er).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_i@type p6@type p4 p6).", + "c p7", + "=> (p7 not_e@type and_i@type not_e p7).", + "c x1", + "=> (x1 and_i@type and_i@type x1 x1).", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "a exfalso", + "=> false.", + "c p7", + "=> (p7 and_er@type p5@type and_er p5).", + "c em", + "=> (em goal4@2@2).", + "c x1", + "=> (x1 iff_el@type iff_er@type iff_el iff_er).", + "c x1", + "=> (x1 em@type p9@type em p9).", + "c p7", + "=> (p7 p6@type p5@type p6 p5).", + "c p7", + "=> (p7 p16@type and_i@type p16 x0).", + "c x1", + "=> (x1 and_el@type not_i@type and_el p4)." + ] + }, + { + "mode": "sample", + 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[('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c em", + "=> (em p@type).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (not 'P) -> 'P -> false])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x", + "=> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> (or 'P (not 'P))]); [(or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[false -> ('P : prop) -> 'P] -> [(or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))) [false -> ('P : prop) -> 'P]); [(or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))) -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em goal7).", + "a or_il", + "=> .", + "intro.", + "c em", + "=> (em goal1).", + "a x", + "=> (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))) (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))) (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) 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-> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))])].", + "c em", + "=> (em goal9).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal8).", + "a not_e", + "=> (not (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]])) (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 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-> (or 'P (not 'P))] (and false (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] false))))); false.", + "a and_i", + "=> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] false)); (and [('P : prop) -> (or 'P (not 'P))] (and false (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] false)))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "intro." + ] + 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_i@type and_el@type x0 and_el).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 667, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x 'B) (and (not x) (not 'B))) (iff x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (or (and x 'B) (and (not x) (not 'B))) (iff x 'B))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em 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'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))); (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [false -> ('P : prop) -> 'P]))); (not (not [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not (not [false -> ('P : prop) -> 'P])))].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3362, + "actions": [ + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x1", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "intro.", + "c em", + "=> (em false).", + "intro.", + "c x3", + "=> (x3 goal6 and_el@type and_el).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a x0", + "=> false.", + "c x3", + "=> (x3 p7@type@2 and_i@type and_i).", + "a not_e", + "=> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 em@type p8@type p8).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 403, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]]; [(not [false -> ('P : prop) -> 'P]) -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]]); [[false -> ('P : prop) -> 'P] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]].", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em goal6).", + "a x", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[false -> ('P : prop) -> 'P] -> false])].", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]; [(not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]].", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]]; [(not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]) -> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 x).", + "c x1", + "=> (x1 exfalso).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c x", + "=> (x and_el).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c em", + "=> (em goal13).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c x", + "=> (x x0).", + "intro.", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> (and [[('P : prop) -> (or 'P (not 'P))] -> false] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a exfalso", + "=> .", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 422, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] 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'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_el@type p3@type iff_el p3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el iff_el@type p3@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 goal8).", + "c x0", + "=> (x0 x).", + "c x0", + "=> (x0 p8@type).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type@2).", + "c x0", + "=> (x0 p5@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3250, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a 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(and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + 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-> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [x -> [[[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [x -> [[[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [x -> [[[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "c em" + ] + }, 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false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 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'P)]) -> false])))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 365, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] 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+ "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))).", + "a not_i", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "a x0", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [(or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [(or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [(or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false])].", + "a or_e", + "=> [false -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and [[('P : prop) -> (not 'P) -> 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prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", 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exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P 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[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 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-> ['P -> false] -> (not 'P)]) -> false]].", + "intro.", + "c em", + "=> (em goal6).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1819, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "c x1", + "=> (x1 p@type@2 or_ir@type or_ir).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a not_i", + "=> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false].", + "intro.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not x); x.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 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-> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 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[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]])) false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]])) false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]])) false)))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x1", + "=> (iff false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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'Q)])]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 not_e@type x1 x0).", + "a x", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a exfalso", + "=> .", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 512, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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-> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]]))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]]) (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]]))))].", + "c em", + "=> (em goal).", + "a x", + "=> (iff (not (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]]) (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]])))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a iff_i", + "=> [(not (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]]) (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : 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prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + 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'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)])); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 631, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(or x 'C) -> (or 'B 'D)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(or x 'C) -> (or 'B 'D)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(or x 'C) -> (or 'B 'D)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(or x 'C) -> (or 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prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em goal5).", + "a x", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))] -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]) -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal17).", + "a x", + "=> false.", + "c em", + "=> (em p4@type).", + "c x1", + "=> (x1 p).", + "a x", + "=> false.", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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-> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))])]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])); [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and x [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> x; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 618, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal7).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3490, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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-> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P])))).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))))]; [(not [false -> ('P : prop) -> 'P]) -> (not (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))))].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type@2 and_i@type and_i).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x1", + "=> (x1 goal p0@type p0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6215, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x1", + "=> (x1 or_e@type iff_i@type or_e iff_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type iff_i@type p1).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> false].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]))].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a p4", + "=> (or (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 51, + "evals_used": 43182, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x not_i@type goal8 goal8)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..692080173f0d5666070d652f73a0625e923fb7d1 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,857 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_3 (traces=17 evals=17468) +[ ] - extrinsic_L0_4 (traces=17 evals=26328) +[ ] - extrinsic_L0_5 (traces=17 evals=33165) +[ ] - extrinsic_L0_1 (traces=8 evals=14103) +[ ] - extrinsic_L0_2 (traces=15 evals=32920) +[ ] - extrinsic_L0_6 (traces=14 evals=24865) +[OK ] - extrinsic_L0_10 (traces=5 evals=3606) +[ ] - extrinsic_L0_7 (traces=17 evals=18890) +[ ] - extrinsic_L0_8 (traces=17 evals=25269) +[ ] - extrinsic_L0_9 (traces=15 evals=30330) +[ ] - extrinsic_L0_11 (traces=14 evals=26718) +[ ] - extrinsic_L0_12 (traces=15 evals=27563) +[ ] - extrinsic_L0_13 (traces=14 evals=39559) +[ ] - extrinsic_L0_14 (traces=6 evals=26670) + +thread '' (641618) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_1 (traces=17 evals=27112) + +thread '' (641618) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_2 (traces=10 evals=15783) + +thread '' (641613) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641613) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_3 (traces=13 evals=25023) + +thread '' (641617) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_4 (traces=13 evals=25885) + +thread '' (641617) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_1 (traces=17 evals=33949) +[ ] - extrinsic_L2_2 (traces=15 evals=25764) +[ ] - extrinsic_L2_3 (traces=17 evals=29357) + +thread '' (641613) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641613) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_7 (traces=17 evals=16619) + +thread '' (641618) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641618) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_4 (traces=17 evals=11809) +[ ] - extrinsic_L2_5 (traces=15 evals=28023) +[ ] - extrinsic_L2_6 (traces=15 evals=16621) +[ ] - extrinsic_L2_8 (traces=15 evals=17982) +[ ] - extrinsic_L2_9 (traces=10 evals=16911) + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_10 (traces=17 evals=19538) + +thread '' (641620) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_11 (traces=14 evals=28861) + +thread '' (641620) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_12 (traces=14 evals=20923) +[ ] - extrinsic_L2_13 (traces=14 evals=26441) +[ ] - extrinsic_L3_1 (traces=14 evals=20190) +[ ] - extrinsic_L3_2 (traces=11 evals=8024) + +thread '' (641613) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641613) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_3 (traces=11 evals=14171) +[ ] - extrinsic_L3_4 (traces=14 evals=20668) +[ ] - extrinsic_L3_5 (traces=17 evals=23789) +[ ] - extrinsic_L3_6 (traces=17 evals=31451) + +thread '' (641616) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641616) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=17 evals=24278) +[ ] - extrinsic_L3_8 (traces=17 evals=28826) +[ ] - extrinsic_L3_12 (traces=17 evals=13054) +[ ] - extrinsic_L3_11 (traces=17 evals=22712) +[ ] - extrinsic_L3_9 (traces=14 evals=22292) +[ ] - extrinsic_L3_10 (traces=12 evals=14762) +[ ] - extrinsic_L3_14 (traces=17 evals=12940) +[ ] - extrinsic_L3_13 (traces=17 evals=23922) +[ ] - extrinsic_L3_15 (traces=13 evals=24137) +[ ] - extrinsic_L3_16 (traces=12 evals=20341) +[ ] - extrinsic_L3_17 (traces=16 evals=29903) +[ ] - extrinsic_L3_19 (traces=10 evals=8509) +[ ] - extrinsic_L3_18 (traces=17 evals=25211) +[ ] - extrinsic_L3_20 (traces=13 evals=28468) +[ ] - extrinsic_L3_25 (traces=17 evals=12456) +[ ] - extrinsic_L3_23 (traces=17 evals=20322) +[ ] - extrinsic_L3_21 (traces=17 evals=16636) +[ ] - extrinsic_L3_22 (traces=15 evals=28074) +[ ] - extrinsic_L3_24 (traces=17 evals=27131) +[ ] - extrinsic_L3_27 (traces=17 evals=22169) +[ ] - extrinsic_L3_26 (traces=13 evals=26364) + +thread '' (641620) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_28 (traces=6 evals=10338) +[ ] - extrinsic_L3_29 (traces=13 evals=21458) +[ ] - extrinsic_L4_1 (traces=17 evals=22940) +[ ] - extrinsic_L4_2 (traces=14 evals=29056) +[ ] - extrinsic_L4_3 (traces=15 evals=30105) +[ ] - extrinsic_L4_6 (traces=17 evals=24703) +[ ] - extrinsic_L4_4 (traces=13 evals=24738) +[ ] - extrinsic_L4_5 (traces=14 evals=28608) +[ ] - extrinsic_L4_7 (traces=13 evals=30565) +[ ] - extrinsic_L4_8 (traces=13 evals=27467) + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_9 (traces=17 evals=39896) +[ ] - extrinsic_L4_10 (traces=14 evals=29847) +[ ] - extrinsic_L4_11 (traces=14 evals=21127) + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641613) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_12 (traces=15 evals=22444) +[ ] - extrinsic_L4_14 (traces=17 evals=15336) +[ ] - extrinsic_L4_13 (traces=15 evals=28156) +[ ] - extrinsic_L5_2 (traces=17 evals=26111) +[ ] - extrinsic_L5_1 (traces=8 evals=13447) +[ ] - extrinsic_L5_3 (traces=17 evals=19103) +[ ] - extrinsic_L5_4 (traces=15 evals=24550) +[ ] - extrinsic_L5_5 (traces=14 evals=12223) +[ ] - extrinsic_L5_6 (traces=14 evals=32235) +[ ] - extrinsic_L5_7 (traces=10 evals=24275) + +thread '' (641617) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641617) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641617) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=13 evals=19324) +[ ] - extrinsic_L5_8 (traces=8 evals=14718) +[ ] - extrinsic_L5_10 (traces=17 evals=19236) +[ ] - extrinsic_L6_1 (traces=7 evals=12250) +[ ] - extrinsic_L5_11 (traces=8 evals=134377) +[ ] - extrinsic_L6_2 (traces=8 evals=31384) + +thread '' (641618) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641618) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641619) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_4 (traces=13 evals=33518) +[ ] - extrinsic_L6_6 (traces=17 evals=16891) +[ ] - extrinsic_L6_5 (traces=15 evals=20183) +[ ] - extrinsic_L6_8 (traces=17 evals=20637) +[ ] - extrinsic_L6_7 (traces=17 evals=22722) +[ ] - extrinsic_L6_9 (traces=9 evals=54789) +[ ] - extrinsic_L6_3 (traces=3 evals=62457) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 1/94 in 9474.0s diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..b4be7c374f8b4b9388ef2bae04e6039c61e46895 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log @@ -0,0 +1,201 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_3 (traces=17 evals=16983) +[ ] - extrinsic_L0_1 (traces=17 evals=24092) +[ ] - extrinsic_L0_4 (traces=17 evals=28357) +[ ] - extrinsic_L0_2 (traces=17 evals=29752) +[ ] - extrinsic_L0_5 (traces=17 evals=33176) +[ ] - extrinsic_L0_6 (traces=14 evals=38101) +[OK ] - extrinsic_L0_10 (traces=5 evals=2759) +[ ] - extrinsic_L0_7 (traces=17 evals=17761) +[ ] - extrinsic_L0_8 (traces=17 evals=23140) +[ ] - extrinsic_L0_11 (traces=17 evals=27159) +[ ] - extrinsic_L0_9 (traces=13 evals=25433) +[ ] - extrinsic_L0_12 (traces=17 evals=26007) +[ ] - extrinsic_L0_13 (traces=11 evals=27934) +[ ] - extrinsic_L0_14 (traces=17 evals=24756) +[ ] - extrinsic_L1_2 (traces=17 evals=14665) +[ ] - extrinsic_L1_3 (traces=17 evals=20667) +[ ] - extrinsic_L1_1 (traces=17 evals=24701) +[ ] - extrinsic_L2_1 (traces=17 evals=21921) +[ ] - extrinsic_L1_4 (traces=15 evals=26322) +[ ] - extrinsic_L2_2 (traces=10 evals=17657) +[ ] - extrinsic_L2_4 (traces=17 evals=20561) +[ ] - extrinsic_L2_3 (traces=16 evals=18800) + +thread '' (924242) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_5 (traces=15 evals=25025) +[ ] - extrinsic_L2_6 (traces=16 evals=27272) +[ ] - extrinsic_L2_7 (traces=17 evals=38208) +[ ] - extrinsic_L2_9 (traces=17 evals=18208) +[ ] - extrinsic_L2_8 (traces=16 evals=24102) +[ ] - extrinsic_L2_10 (traces=12 evals=24565) +[ ] - extrinsic_L2_11 (traces=17 evals=25759) +[ ] - extrinsic_L2_12 (traces=12 evals=17512) +[ ] - extrinsic_L2_13 (traces=13 evals=23544) +[ ] - extrinsic_L3_1 (traces=8 evals=5593) +[ ] - extrinsic_L3_2 (traces=15 evals=38367) +[ ] - extrinsic_L3_3 (traces=15 evals=26138) +[ ] - extrinsic_L3_6 (traces=17 evals=22848) +[ ] - extrinsic_L3_4 (traces=13 evals=25676) +[ ] - extrinsic_L3_5 (traces=17 evals=26556) +[ ] - extrinsic_L3_7 (traces=17 evals=19759) +[ ] - extrinsic_L3_8 (traces=17 evals=19802) +[ ] - extrinsic_L3_9 (traces=17 evals=29064) +[ ] - extrinsic_L3_11 (traces=17 evals=26500) +[ ] - extrinsic_L3_12 (traces=17 evals=19253) +[ ] - extrinsic_L3_10 (traces=12 evals=29304) +[ ] - extrinsic_L3_13 (traces=17 evals=28131) + +thread '' (924243) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_16 (traces=17 evals=20646) +[ ] - extrinsic_L3_14 (traces=15 evals=23906) +[ ] - extrinsic_L3_15 (traces=13 evals=27193) +[ ] - extrinsic_L3_17 (traces=13 evals=33214) +[ ] - extrinsic_L3_18 (traces=17 evals=23161) +[ ] - extrinsic_L3_19 (traces=17 evals=23849) +[ ] - extrinsic_L3_20 (traces=14 evals=30658) +[ ] - extrinsic_L3_21 (traces=8 evals=17834) +[ ] - extrinsic_L3_22 (traces=14 evals=23593) +[ ] - extrinsic_L3_24 (traces=17 evals=27248) +[ ] - extrinsic_L3_23 (traces=11 evals=19272) +[ ] - extrinsic_L3_25 (traces=17 evals=25297) +[ ] - extrinsic_L3_28 (traces=17 evals=15333) + +thread '' (924244) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_27 (traces=15 evals=29349) +[ ] - extrinsic_L3_26 (traces=4 evals=7442) +[ ] - extrinsic_L3_29 (traces=11 evals=15777) +[ ] - extrinsic_L4_1 (traces=15 evals=19399) + +thread '' (924241) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L4_2 (traces=17 evals=24335) +[ ] - extrinsic_L4_3 (traces=17 evals=26881) +[ ] - extrinsic_L4_5 (traces=17 evals=32550) +[ ] - extrinsic_L4_6 (traces=17 evals=24300) +[ ] - extrinsic_L4_4 (traces=14 evals=22777) +[ ] - extrinsic_L4_7 (traces=15 evals=22386) +[ ] - extrinsic_L4_9 (traces=17 evals=15327) +[ ] - extrinsic_L4_8 (traces=13 evals=26824) +[ ] - extrinsic_L4_10 (traces=17 evals=24277) +[ ] - extrinsic_L4_11 (traces=12 evals=20666) + +thread '' (924240) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L4_12 (traces=17 evals=28269) +[ ] - extrinsic_L4_14 (traces=17 evals=19413) +[ ] - extrinsic_L4_13 (traces=14 evals=27560) +[ ] - extrinsic_L5_1 (traces=15 evals=28487) +[ ] - extrinsic_L5_2 (traces=12 evals=25008) +[ ] - extrinsic_L5_3 (traces=17 evals=23071) +[ ] - extrinsic_L5_4 (traces=15 evals=28678) +[ ] - extrinsic_L5_6 (traces=17 evals=27319) +[ ] - extrinsic_L5_7 (traces=3 evals=25819) +[ ] - extrinsic_L5_8 (traces=11 evals=26584) +[ ] - extrinsic_L5_5 (traces=1 evals=608) +[ ] - extrinsic_L5_9 (traces=15 evals=30147) +[ ] - extrinsic_L5_10 (traces=3 evals=18367) +[ ] - extrinsic_L5_11 (traces=8 evals=51016) +[ ] - extrinsic_L6_1 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}, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25919, + "max_open": 21920, + "solution_actions": null, + "problem": "extrinsic_L4_13" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26367, + "max_open": 22368, + "solution_actions": null, + "problem": "extrinsic_L4_14" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25871, + "max_open": 21872, + "solution_actions": null, + "problem": "extrinsic_L5_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26198, + "max_open": 22199, + "solution_actions": null, + "problem": "extrinsic_L5_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26268, + "max_open": 22269, + "solution_actions": null, + "problem": "extrinsic_L5_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25788, + "max_open": 21789, + "solution_actions": null, + "problem": "extrinsic_L5_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26518, + "max_open": 22519, + "solution_actions": null, + "problem": "extrinsic_L5_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26094, + "max_open": 22095, + "solution_actions": null, + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26493, + "max_open": 22494, + "solution_actions": null, + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26439, + "max_open": 22440, + "solution_actions": null, + "problem": "extrinsic_L5_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26269, + "max_open": 22270, + "solution_actions": null, + "problem": "extrinsic_L5_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26546, + "max_open": 22547, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31246, + "max_open": 27247, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26057, + "max_open": 22058, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31327, + "max_open": 27328, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31305, + "max_open": 27306, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31217, + "max_open": 27218, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30982, + "max_open": 26983, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25985, + "max_open": 21986, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25980, + "max_open": 21981, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31332, + "max_open": 27333, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31061, + "max_open": 27062, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..30228f65dbcd31daa0d29224a786f05264197fee --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=5 evals=25 maxopen=19) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_3 (solved pops=62 evals=371 maxopen=310) +[OK ] extrinsic_L0_5 (solved pops=56 evals=368 maxopen=313) +[OK ] extrinsic_L0_10 (solved pops=7 evals=41 maxopen=35) +[OK ] extrinsic_L0_6 (solved pops=57 evals=353 maxopen=297) +[OK ] extrinsic_L0_9 (solved pops=54 evals=352 maxopen=283) +[OK ] extrinsic_L0_7 (solved pops=56 evals=356 maxopen=301) +[OK ] extrinsic_L0_8 (solved pops=58 evals=361 maxopen=304) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=22 evals=156 maxopen=135) +[OK ] extrinsic_L0_4 (solved pops=209 evals=1104 maxopen=896) +[OK ] extrinsic_L1_4 (solved pops=20 evals=124 maxopen=103) +[OK ] extrinsic_L0_11 (solved pops=211 evals=1143 maxopen=933) +[OK ] extrinsic_L1_1 (solved pops=222 evals=1220 maxopen=981) +[OK ] extrinsic_L1_2 (solved pops=462 evals=2457 maxopen=1996) +[OK ] extrinsic_L1_3 (solved pops=462 evals=2454 maxopen=1993) +[OK ] extrinsic_L2_1 (solved pops=1256 evals=6845 maxopen=5590) +[OK ] extrinsic_L2_6 (solved pops=1632 evals=9398 maxopen=7767) +[OK ] extrinsic_L2_7 (solved pops=1027 evals=5748 maxopen=4722) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25960 maxopen=21961) +[OK ] extrinsic_L0_14 (solved pops=3964 evals=25999 maxopen=22036) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25844 maxopen=21845) +[OK ] extrinsic_L2_11 (solved pops=22 evals=145 maxopen=122) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25839 maxopen=21840) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25734 maxopen=21735) +[OK ] extrinsic_L2_9 (solved pops=1015 evals=5694 maxopen=4680) +[OK ] extrinsic_L2_12 (solved pops=1352 evals=7666 maxopen=6315) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26006 maxopen=22007) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26379 maxopen=22380) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25815 maxopen=21816) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25859 maxopen=21860) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25853 maxopen=21854) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25903 maxopen=21904) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26045 maxopen=22046) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26039 maxopen=22040) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25736 maxopen=21737) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25835 maxopen=21836) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25975 maxopen=21976) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26186 maxopen=22187) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25952 maxopen=21953) +[ ] extrinsic_L3_11 (budget pops=4000 evals=26206 maxopen=22207) +[OK ] extrinsic_L3_13 (solved pops=3497 evals=22185 maxopen=18689) +[OK ] extrinsic_L3_14 (solved pops=3216 evals=19687 maxopen=16472) +[ ] extrinsic_L3_12 (budget pops=4000 evals=26210 maxopen=22211) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26009 maxopen=22010) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26033 maxopen=22034) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25733 maxopen=21734) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25410 maxopen=21411) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26010 maxopen=22011) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26157 maxopen=22158) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26056 maxopen=22057) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25817 maxopen=21818) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26296 maxopen=22297) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26105 maxopen=22106) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26647 maxopen=22648) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25955 maxopen=21956) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26274 maxopen=22275) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25796 maxopen=21797) +[ ] extrinsic_L4_1 (budget pops=4000 evals=25551 maxopen=21552) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26838 maxopen=22839) +[ ] extrinsic_L4_2 (budget pops=4000 evals=25864 maxopen=21865) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26040 maxopen=22041) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25965 maxopen=21966) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26132 maxopen=22133) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25952 maxopen=21953) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26675 maxopen=22676) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26501 maxopen=22502) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26704 maxopen=22705) +[OK ] extrinsic_L4_12 (solved pops=1317 evals=7264 maxopen=5945) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25310 maxopen=21311) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26341 maxopen=22342) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25919 maxopen=21920) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26367 maxopen=22368) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25871 maxopen=21872) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26198 maxopen=22199) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26268 maxopen=22269) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25788 maxopen=21789) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26518 maxopen=22519) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26094 maxopen=22095) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26493 maxopen=22494) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26439 maxopen=22440) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26269 maxopen=22270) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26546 maxopen=22547) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26057 maxopen=22058) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31246 maxopen=27247) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31327 maxopen=27328) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31305 maxopen=27306) +[ ] extrinsic_L6_4 (budget pops=4000 evals=31217 maxopen=27218) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30982 maxopen=26983) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25985 maxopen=21986) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25980 maxopen=21981) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31332 maxopen=27333) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31061 maxopen=27062) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] 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"extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25805, + "max_open": 21806, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25755, + "max_open": 21756, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31336, + "max_open": 27337, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30989, + "max_open": 26990, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..3213c559f847211388919723a2559cdf202a2045 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_5 (solved pops=53 evals=321 maxopen=269) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_7 (solved pops=55 evals=354 maxopen=300) +[OK ] extrinsic_L0_6 (solved pops=51 evals=316 maxopen=266) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_3 (solved pops=78 evals=449 maxopen=372) +[OK ] extrinsic_L0_13 (solved pops=23 evals=171 maxopen=149) +[OK ] extrinsic_L0_9 (solved pops=49 evals=328 maxopen=264) +[OK ] extrinsic_L0_8 (solved pops=53 evals=349 maxopen=297) +[OK ] extrinsic_L0_4 (solved pops=224 evals=1209 maxopen=986) +[OK ] extrinsic_L1_4 (solved pops=17 evals=105 maxopen=87) +[OK ] extrinsic_L0_11 (solved pops=224 evals=1213 maxopen=990) +[OK ] extrinsic_L1_1 (solved pops=221 evals=1204 maxopen=966) +[OK ] extrinsic_L1_2 (solved pops=510 evals=2758 maxopen=2249) +[OK ] extrinsic_L1_3 (solved pops=511 evals=2772 maxopen=2262) +[OK ] extrinsic_L2_1 (solved pops=1257 evals=6961 maxopen=5705) +[OK ] extrinsic_L2_6 (solved pops=1690 evals=9917 maxopen=8228) +[OK ] extrinsic_L2_7 (solved pops=998 evals=5686 maxopen=4689) +[OK ] extrinsic_L0_14 (solved pops=3878 evals=25170 maxopen=21293) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25898 maxopen=21899) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25890 maxopen=21891) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25754 maxopen=21755) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25888 maxopen=21889) +[OK ] extrinsic_L2_9 (solved pops=984 evals=5621 maxopen=4638) +[OK ] extrinsic_L2_12 (solved pops=1221 evals=6780 maxopen=5560) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26277 maxopen=22278) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26184 maxopen=22185) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25705 maxopen=21706) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25905 maxopen=21906) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25716 maxopen=21717) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25751 maxopen=21752) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25952 maxopen=21953) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25955 maxopen=21956) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25755 maxopen=21756) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25827 maxopen=21828) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26057 maxopen=22058) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26035 maxopen=22036) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25950 maxopen=21951) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25825 maxopen=21826) +[OK ] extrinsic_L3_14 (solved pops=3163 evals=19551 maxopen=16389) +[OK ] extrinsic_L3_13 (solved pops=3511 evals=22659 maxopen=19149) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25875 maxopen=21876) +[ ] extrinsic_L3_15 (budget pops=4000 evals=25850 maxopen=21851) +[ ] extrinsic_L3_16 (budget pops=4000 evals=25868 maxopen=21869) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25773 maxopen=21774) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25233 maxopen=21234) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25620 maxopen=21621) +[ ] extrinsic_L3_20 (budget pops=4000 evals=25796 maxopen=21797) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25835 maxopen=21836) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25799 maxopen=21800) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26133 maxopen=22134) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26028 maxopen=22029) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25909 maxopen=21910) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26889 maxopen=22890) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26023 maxopen=22024) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25775 maxopen=21776) +[ ] extrinsic_L4_1 (budget pops=4000 evals=25995 maxopen=21996) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26751 maxopen=22752) +[ ] extrinsic_L4_3 (budget pops=4000 evals=25719 maxopen=21720) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26958 maxopen=22959) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25855 maxopen=21856) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25852 maxopen=21853) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26175 maxopen=22176) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26732 maxopen=22733) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26357 maxopen=22358) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25837 maxopen=21838) +[OK ] extrinsic_L4_12 (solved pops=1311 evals=7556 maxopen=6243) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25655 maxopen=21656) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26245 maxopen=22246) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25836 maxopen=21837) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26090 maxopen=22091) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25586 maxopen=21587) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26097 maxopen=22098) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26193 maxopen=22194) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25519 maxopen=21520) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26445 maxopen=22446) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26105 maxopen=22106) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26276 maxopen=22277) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26328 maxopen=22329) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26495 maxopen=22496) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26538 maxopen=22539) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31221 maxopen=27222) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25906 maxopen=21907) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31096 maxopen=27097) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31055 maxopen=27056) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30916 maxopen=26917) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30829 maxopen=26830) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25805 maxopen=21806) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25755 maxopen=21756) +[ ] extrinsic_L6_9 (budget pops=4000 evals=30989 maxopen=26990) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31336 maxopen=27337) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) 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b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..358c80b19a08ed3d96b03cbbff01d2b68e3ea949 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json @@ -0,0 +1,92532 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/epoch_2.pt", + "problemset": "extrinsic-95", + "n_samples": 16, + "max_depth": 60, + "temperature": 1.0, + "greedy_first": true, + "seed": 0, + "workers": 6, + "timeout": 600.0, + "max_actions": 0, + "num_problems": 94, + "num_solved": 1, + "elapsed_sec": 9116.401124715805, + "results": [ + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 23163, + "solution_actions": null, + 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-> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]) -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "intro.", + "c em", + "=> (em goal21).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", 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false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]; [(not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]; [(not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 302, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2273, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]).", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> (or 'P (not 'P))] -> (not [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]." + ] + } + ], + "problem": "extrinsic_L0_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 28158, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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: prop) -> (and 'A 'B) -> 'A])).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A])) -> (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]) [('P : prop) -> ['P -> false] -> (not 'P)]) (or (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A])) (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]))))) (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]))]; [(not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] (not [('A : prop) -> ('B : prop) -> 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-> (and 'A 'B) -> 'A])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1218, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 620, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (and x 'B) -> x]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> 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+ "intro.", + "c em", + "=> (em false).", + "intro.", + "c x3", + "=> (x3 p2@type p1@type p1).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x0", + "=> false.", + "c x3", + "=> (x3 p6@type p6@type p6).", + "a not_e", + "=> (not (not x)); (not x).", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 goal not_e@type not_e).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 502, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 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or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]])]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x", + "=> (x or_ir@type x1 or_ir).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]) -> false].", + "a x", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a and_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; 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'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x goal or_e@type and_el).", + "c x", + "=> (x iff_i@type or_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a 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prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11938, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> x]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> x]].", + "c x0", + "=> (x0 not_i@type em@type not_i em).", + "c x0", + "=> (x0 and_i@type or_il@type x0 or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type em@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 iff_i@type or_il@type iff_i or_il).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c p8", + "=> (p8 exfalso@type and_i@type exfalso and_i).", + "c x1", + "=> (x1 and_i@type and_i@type p8 and_i).", + "c x0", + "=> 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"=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2652, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : 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: prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x0", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))] [('P : prop) -> ['P -> false] -> (not 'P)]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]].", + "c em", + "=> (em p3@type@2).", + "a or_ir", + "=> .", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))] -> [[('P : prop) -> (not 'P) -> 'P 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p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (not false) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> (not false); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4575, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 not_e@type p1@type not_e p1).", + "c and_el", + "=> (and_el not_e@type p1@type p3).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]))).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]])) -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]])) -> false]].", + "c x2", + "=> (x2 exfalso@type p@type exfalso p).", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 p1@type p6@type p1 p6).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 583, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))); (not (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 639, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type@2).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c x", + "=> (x p@type@2).", + "c x", + "=> (x p2@type@2).", + "a exfalso", + "=> false.", + "c x", + "=> (x p3@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c x", + "=> (x not_e@type).", + "a or_e", + "=> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]; [(not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))." + ] + } + ], + "problem": "extrinsic_L0_3" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 24119, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": 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"=> (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x", + "=> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a x", + "=> (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])) false).", + "a x", + "=> (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]).", + "a or_e", + "=> [(and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]; [(not (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (and (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])].", + "a x", + "=> (and [(and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])] false).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "c em", + "=> (em goal9).", + "a and_i", + "=> false; (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(and false [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (and false [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and false [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (and false [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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: prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x goal or_e@type and_i).", + "c x", + "=> (x iff_i@type and_el@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2249, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]] -> false].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [false -> ('P : prop) -> 'P]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]] -> false]]; [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c x", + "=> (x goal p2@type@2 and_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e goal x1 and_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] [false -> ('P : prop) -> 'P])); (or [('P : prop) -> (not 'P) -> 'P -> false] [false -> ('P : prop) -> 'P]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4457, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> 'B -> (and x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c and_el", + "=> (and_el exfalso@type or_ir@type p3).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (and [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "c x2", + "=> (x2 not_e@type p@type x0 p).", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_i@type or_il@type x2 or_il).", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]] -> false].", + "a p4", + "=> false.", + "c em", + "=> (em goal2).", + "c x2", + "=> (x2 exfalso@type p2@type p4 p2).", + "c x2", + "=> (x2 iff_el@type p0@type iff_el p0).", + "a p4", + "=> false.", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_er@type em@type and_er em)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 527, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 p2@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4332, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a 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+ "=> false.", + "a x", + "=> (not (not (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))))); (not (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 451, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a 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'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a x0", + "=> (and [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a x0", + "=> (and (and [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a x0", + "=> (and (and (and [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> 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'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "c not_e", + "=> (not_e exfalso@type x1 x0).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c 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prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [false -> ('P : prop) -> 'P]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> 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prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2291, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal16 or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + 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(iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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-> (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9744, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> 'B -> 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-> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type p@type p0 p).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false) (and false (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [false -> ('P : prop) -> 'P] false) false)))))))].", + "a x", + "=> (and [false -> ('P : prop) -> 'P] [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> 'Q 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'P])))]]) (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]])).", + "a exfalso", + "=> false.", + "a x", + "=> (not (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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: prop) -> 'P -> 'Q -> (and 'P 'Q)] false)]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]) -> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)].", + "a x", + "=> (iff [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x goal not_i@type iff_el).", + "c x", + "=> (x iff_i@type or_ir@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2210, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[false -> false] -> false]; [(not [false -> false]) -> false].", + "c x", + "=> (x goal p2@type@2 iff_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 516, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]; [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]; [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a or_e", + "=> 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))])); (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]))).", + "a and_i", + "=> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> 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+ "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]))]]).", + "a and_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]))]].", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]))]]).", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]))]])).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]].", + "a exfalso", + "=> false.", + "a x1", + "=> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]))) false).", + "a x1", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]))) false)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false]; (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]])))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]))))]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7651, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type p3@type@2 not_e).", + "c x0", + "=> (x0 exfalso@type or_ir@type exfalso).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> 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-> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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-> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1994, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 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-> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x goal goal16 not_e).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 332, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not false) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not false) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5060, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not x) -> x -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 exfalso@type goal exfalso not_e).", + "c and_el", + "=> (and_el exfalso@type not_e@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "c em", + "=> (em iff_i@type).", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_i@type or_ir@type and_i or_ir).", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a p4", + "=> false.", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 iff_i@type goal iff_i not_e).", + "c x2", + "=> (x2 iff_er@type p2@type iff_er p2).", + "a p4", + "=> false.", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_er@type p5@type and_er p5)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1392, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 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'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not 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-> (or 'P (not 'P))] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])]; [(not [false -> ('P : prop) -> 'P]) -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])].", + "intro.", + "a x0", + "=> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [false -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])].", + "a x0", + "=> (or [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (or [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (or [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] x); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> (or [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> 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(or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> (or [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])) x); [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> (or [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> (or [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])) -> [[false -> ('P : prop) -> 'P] -> false]]; [x -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x1", + "=> false." + ] + }, + { + "mode": "sample", + 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> false]].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 519, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> 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prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('A : prop) -> (or 'A (not 'A))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])])].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false]; [(not (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> false]; [(not [('A : prop) -> (or 'A (not 'A))]) -> false].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('A : prop) -> (or 'A (not 'A))] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> [[('A : prop) -> (or 'A (not 'A))] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x goal or_e@type em).", + "c x", + "=> (x iff_i@type and_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('A : prop) -> (or 'A (not 'A))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('A : prop) -> (or 'A (not 'A))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7373, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [false -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> (or 'P (not 'P))] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 990, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x1", + "=> (x1 and_el@type not_e@type not_e).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11018, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_ir", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal2).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> 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-> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not false) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not false) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not false) -> false]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not false) -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 983, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2186, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal16 not_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1326, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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false]].", + "c em", + "=> (em or_ir@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0" + ] + } + ], + "problem": "extrinsic_L1_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 29667, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) 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'B]]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + 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"a or_il", + "=> [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal2).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em p@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))]; [(or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))].", + "a x", + "=> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))); [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))) -> false].", + "c em", + "=> (em goal9).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]].", + "intro.", + "c em", + "=> (em goal4).", + "a x", + "=> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (or (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]) (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P])))); [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> [('B : prop) -> [(not x0) -> [x0 -> 'B]]]]; [(or (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]) (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]))) -> [('B : prop) -> [(not x0) -> [x0 -> 'B]]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (or (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]) (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]))))]; [[('P : prop) -> (or 'P (not 'P))] -> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (or (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]) (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 557, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 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-> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em x).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not (not false)); (not false).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[[('P : prop) 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false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[false -> false] -> false]; [(not [false -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); false.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 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-> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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-> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a p4", 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(not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]]))]] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a x1", + "=> (and (and false (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]]))]] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> 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(not [[false -> ('P : prop) -> 'P] -> false]))).", + "a not_i", + "=> [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5938, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type em@type x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]) false); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [false -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 627, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or false (not false))).", + "a or_e", + "=> [false -> (not (or false (not false)))]; [(not false) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [false -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or false (not false))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2418, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p0@type p0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal11 iff_er@type iff_er).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))))).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))) -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))))]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 436, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not 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"c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5586, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))])].", + "c x0", + "=> (x0 or_ir@type goal2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em exfalso@type).", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em goal7).", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p0@type@2).", + "a x0", + "=> false.", + "a x0", + "=> false.", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2418, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type and_i@type and_i).", + "a not_e", + "=> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]); [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal11 iff_er@type iff_er).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4266, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not [('P : 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-> (and 'P 'Q) -> 'Q] -> false]].", + "c x", + "=> (x exfalso@type p1@type@2 exfalso).", + "c x", + "=> (x em@type not_i@type em).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type goal1 p0).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c x", + "=> (x or_ir@type p2@type or_ir).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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'Q) -> 'P]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 871, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + 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false].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false]].", + "a x1", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6215, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])].", + "c x1", + "=> (x1 or_e@type iff_i@type or_e iff_i).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type iff_i@type p1).", + "a not_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a p4", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [false -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))))) -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a p4", + "=> (or (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[false -> ('P : prop) -> 'P] -> false] [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[false -> ('P : prop) -> 'P] -> false] [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + "evals_used": 1522, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il" + ] + } + ], + "problem": "extrinsic_L2_3" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 23928, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1178, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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'P 'Q)])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4127, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal6).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])]].", + "a or_ir", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]) -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]].", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]] x0).", + "a x2", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]] x0) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x2", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]] x0) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]] x0)); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]] x0) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [(and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]] x0) -> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]] x0) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 329, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> (not [[false -> ('P : prop) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> (not 'P) -> 'P -> false]); [false -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + 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-> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L2_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 27990, + 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prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]) -> (not [('P : prop) 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-> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]) -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1405, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [false -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[false -> ('P : prop) -> 'P] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1460, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (or false (not false)))]; [(not false) -> (not (or false (not false)))].", + "a or_e", + "=> [false -> [false -> (not (or false (not false)))]]; [(not false) -> [false -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_ir@type and_er or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 30, + "evals_used": 610, + "actions": [ + 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'R]))]]; [(not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "a x1", + "=> (and (not [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> (or 'P (not 'P))]).", + "a x1", + "=> (and (not x0) x0).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 402, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + 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'B]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])) -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]); [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7303, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]] false); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]; [false -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]])].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 370, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 45, + "evals_used": 3905, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e" + ] + } + ], + "problem": "extrinsic_L2_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 12131, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + 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(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [('P : prop) -> ('Q : 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not 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"intro.", + "c not_e", + "=> (not_e iff_el@type x1 iff_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 309, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x1", + "=> (iff (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 396, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a exfalso", + "=> 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false))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1417, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> 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'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 goal1 exfalso@type exfalso)." + ] + } + ], + "problem": "extrinsic_L2_7" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 15136, + "solution_actions": null, + "traces": [ + { + "mode": 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-> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff (or 'A 'A) 'A)]); [('A : prop) -> (iff (or 'A 'A) 'A)].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1945, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> 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+ "c em", + "=> (em not_i@type).", + "intro.", + "a x0", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] [(and x false) -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)].", + "c em", + "=> (em goal0@1).", + "c x3", + "=> (x3 p5@type).", + "intro.", + "a iff_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [false -> [('P : prop) -> ['P -> false] -> (not 'P)]].", + "intro.", + "a not_e", + "=> (not (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)); (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a x5", + "=> [(iff [('P : prop) -> ['P -> false] -> (not 'P)] false) -> false].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 473, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p0@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x", + "=> (x and_i@type x1 and_i).", + "a exfalso", + "=> .", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p1@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> (iff (and 'A false) false)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6789, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('A : prop) -> (iff (and 'A false) false)] -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 309, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a x1", + "=> (iff (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [false -> (iff (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not false) -> (iff (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3262, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c x0", + "=> (x0 or_ir@type iff_i@type or_ir iff_i).", + "c and_el", + "=> (and_el or_ir@type iff_i@type p1).", + "a exfalso", + "=> false.", + "c and_er", + "=> (and_er or_ir@type iff_i@type p1).", + "c p2", + "=> (p2 goal4 x x1).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c p2", + "=> (p2 goal0@1 p0@type p0).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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-> false] -> (not (or (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))))]].", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))))]]]; [(not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) (not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))))]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "a exfalso", + "=> false.", + "a x", + "=> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a x2", + "=> [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] -> false].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 342, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 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false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]); [('A 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-> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 629, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> 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-> [x -> x]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [x -> x]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal1).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 goal16 p3@type p3).", + "a or_e", + "=> [[x -> x] -> false]; [(not [x -> x]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [x -> x]]] -> [[x -> x] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [x -> x]]]) -> [[x -> x] -> false]].", + "c x1", + "=> (x1 p@type@2 p0@type p0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff 'A 'A)]].", + "intro.", + "intro.", + "a iff_i", + "=> [x0 -> x0]; [x0 -> x0].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x0 -> x0]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal9).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a x3", + "=> (and (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 424, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> (iff 'A 'A)] -> false]; [(not [('A : prop) -> (iff 'A 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c iff_er", + "=> (iff_er not_i@type not_i@type p5).", + "a or_e", + "=> [[('A : prop) -> (iff 'A 'A)] -> false]; [(not [('A : prop) -> (iff 'A 'A)]) -> false].", + "a x0", + "=> (and [[('A : prop) -> (iff 'A 'A)] -> false] [[('A : prop) -> (iff 'A 'A)] -> false]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff 'A 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", 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-> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + 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false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]].", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]]).", + "a x2", + "=> (and [false -> ('P : prop) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]])).", + "a x2", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and [false -> ('P : prop) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]]))).", + "a x1", + "=> (and x0 (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and [false -> ('P : prop) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]])))).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6404, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e not_i@type x0 not_i).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + 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-> ['P -> 'Q]])] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])))))).", + "a p6" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 346, + "actions": [ + "intro.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "c em", + "=> (em goal14).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "intro.", + "a or_e", + "=> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) 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false] -> (not 'P)]) -> false]]; [(not false) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]].", + "a x1", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (iff false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a iff_i", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))); (not (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a not_i", + "=> [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 331, + "actions": [ + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + 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-> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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+ "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "c x", + "=> (x p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false].", + "intro.", + "c x0", + "=> (x0 iff_er).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em em@type).", + "c x", + "=> (x p0@type and_er@type and_er).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 421, + "actions": [ + "intro.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> (not (not [false -> ('P : prop) -> 'P]))]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> (not (not [false -> ('P : prop) -> 'P]))]].", + "c em", + "=> (em x).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> (not (not [false -> ('P : prop) -> 'P]))]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]] -> (not (not [false -> ('P : prop) -> 'P]))]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "c x3", + "=> (x3 not_i).", + "c x3", + "=> (x3 x0).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "c x2", + "=> (x2 not_i).", + "c p7", + "=> (p7 and_er)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 520, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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prop) -> (or 'P (not 'P))])) -> false]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not false) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]]]; [(not (not false)) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal8).", + "a or_e", + 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]]; [(or [('P : 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'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 671, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> (or 'P (not 'P))] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a exfalso", 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-> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)].", + "intro.", + "a x0", + "=> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)).", + "a x", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))]).", + "c em" + ] + } + ], + "problem": "extrinsic_L3_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 24133, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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'P))] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)) false))))) false).", + "c em", + "=> (em goal12).", + "a and_i", + "=> (and [false -> ('P : prop) -> 'P] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and false (and (and [('P : prop) -> (or 'P (not 'P))] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)) false))))); false.", + "a and_i", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and false (and (and [('P : prop) -> (or 'P (not 'P))] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)) false)))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) -> false]; [(not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 557, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [false -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [false -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [false -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [false -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [false -> false])]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [false -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [false -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 382, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 500, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] false).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p5@type).", + "a iff_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [false -> [('P : prop) -> (not 'P) -> 'P -> false]].", + "a x0", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] false).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type)." + ] + }, + { + "mode": 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x0", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : 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prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e p@type x1 p).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> [false -> false]]]; [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + 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-> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "intro.", + "c x1", + "=> (x1 x0).", + "intro.", + "a not_e", + "=> (not (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))); (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 670, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q 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(not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]])); (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false] (not (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]))).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false]; (not (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]])).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1390, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]); [(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 365, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 640, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> (not 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a x0", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]; [(not (not [false -> ('P : prop) -> 'P])) -> (and [('P : prop) -> ['P -> 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-> [(not [false -> ('P : prop) -> 'P]) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]].", + "intro.", + "c em", + "=> (em not_i@type).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> 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false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; 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(not 'B)] -> ['B -> (not 'A)]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "intro.", + "c em", + "=> (em goal15).", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c em", + "=> (em goal18).", + "a x2", + "=> (or (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])].", + "c x3", + "=> (x3 em@type p1@type em p1).", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + 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-> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) 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'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : 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prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)]); [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + } + ], + "problem": "extrinsic_L3_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + 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-> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "c em", + "=> (em 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(not [('P : prop) -> (or 'P (not 'P))])) [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]).", + "c em", + "=> (em p1@type@2).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false] (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5584, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]; [(not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x0", + "=> .", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]]].", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", 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-> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]].", + "c x1", + "=> (x1 not_e@type and_er@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 435, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]); [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])])))]; [(not [false -> ('P : prop) -> 'P]) -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])])))].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] -> [[false -> ('P : prop) -> 'P] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])])))]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]) -> [[false -> ('P : prop) -> 'P] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])])))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] -> [[false -> ('P : prop) -> 'P] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])])))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] -> [[false -> ('P : prop) -> 'P] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> 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'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ['P -> false] -> (not 'P)]); [false -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and (not false) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> (not false); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, 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(and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2569, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 not_i@type and_el@type and_el).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "a or_e", + "=> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 goal8 or_ir@type x0).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)]].", + "intro.", + "intro.", + "a or_e", + "=> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 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prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2420, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 not_i@type and_i@type and_i).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal10 iff_er@type iff_er).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 674, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 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: prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])])) -> false].", + "a x", + "=> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]) -> false] [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]) -> false]).", + "a and_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]) -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 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1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))))]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1983, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 621, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal7).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2234, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + 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-> (or 'A 'B) -> [(not 'B) -> 'A]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) (not [('P : prop) -> (or 'P (not 'P))])); [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> (or 'P (not 'P))]) (not [('P : prop) -> (or 'P (not 'P))]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> (or (not [('P : prop) -> (or 'P (not 'P))]) (not [('P : prop) -> (or 'P (not 'P))]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9118, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : 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not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff (not x) [x -> false])); (iff (not x) [x -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> (or 'P (not 'P))]); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> .", + "intro.", + "c em", + "=> (em goal2).", + "a x", + "=> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> 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-> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 450, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not false) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [false -> [false -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not false) -> [false -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 631, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(and x (or x x2)) -> x]; [x -> (and x (or x x2))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 635, + "actions": [ + 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(em goal10).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3067, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em or_ir@type).", + "a 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false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em goal2).", + "c em", + "=> (em and_el@type).", + "intro.", + "a x0", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a iff_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [false -> [('P : prop) -> (not 'P) -> 'P -> false]].", + "c em", + "=> (em and_er@type).", + "c x", + "=> (x or_ir@type or_ir@type or_ir).", + "c x", + "=> (x p0@type@2 exfalso@type exfalso).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x", + "=> (x p2@type and_el@type and_el)." + ] + } + ], + "problem": "extrinsic_L3_18" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 11, + "evals_used": 7599, + "solution_actions": null, + 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('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": 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[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em" + ] + } + ], + "problem": "extrinsic_L3_19" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 22588, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> 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'A (or 'B 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))].", + "a or_e", + "=> [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))])]; [(not false) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> 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-> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false])].", + "intro.", + "a not_i", + "=> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false] -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 579, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a 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(and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) false).", + "a x", + "=> (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) false) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))).", + "a x", + "=> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) false) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) (or (not [('P : prop) -> ('Q : prop) -> (and 'P 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'Q]))].", + "a x", + "=> (and [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) false) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a or_e", + "=> [(and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 520, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "intro.", + "c not_e", + "=> (not_e or_ir@type x0 or_ir).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 443, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and false false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "intro.", + "a x0", + "=> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] false).", + "c not_e", + "=> (not_e and_i@type x2 and_i).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2802, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "intro.", + "a x1", + "=> (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 416, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [false -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + 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['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 6872, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]]].", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13)." + ] + } + ], + "problem": "extrinsic_L3_20" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 6, + "evals_used": 2767, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 328, + "actions": [ + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p0@type).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "c em", + "=> (em p1@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 566, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))).", + "a x", + "=> (and (and false (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and [('P : prop) -> ['P -> false] -> (not 'P)] false))))).", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)) (and (and false (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))))).", + "a x", + "=> (and (or (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 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(or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])))) (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)) (and (and false (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))))))]); false.", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> (and (or (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])) (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 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prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 321, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a not_i", + "=> [[(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false] -> false].", + "c em", + "=> (em p2@type).", + "intro.", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", 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[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5355, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal6).", + "a x1", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_ir", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]].", + "a or_e", + "=> [[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]])]; [(not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]])].", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]])]]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]])]].", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]])]]]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not x0); x0.", + "a exfalso", + "=> false.", + "a x1", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) x0); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [x0 -> false].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) x0)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) x0)].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 413, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1886, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "c x", + "=> (x p1@type p1@type p1).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal17).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 632, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + 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-> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x1", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p1@type@2).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "intro.", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]; [(not (not (or [('P : prop) -> 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-> 'Q]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c em", + "=> (em p0@type).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 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(not 'P) -> 'P -> false] -> false])])))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])])))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 403, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> 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false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]; [(not [('P : prop) -> ('Q : prop) 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false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]; [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em iff_i@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]; [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false].", + "c x0", + "=> (x0 exfalso@type and_er@type exfalso and_er).", + "c and_er", + "=> (and_er exfalso@type and_er@type p7)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1390, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not 'A)) -> false]); [('A : prop) -> (iff 'A (not 'A)) -> false].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> (iff 'A (not 'A)) -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> (iff 'A (not 'A)) -> false])].", + "intro.", 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prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + 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"mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + 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-> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a x0", + "=> (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [false -> ('P : prop) -> 'P]) -> (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 396, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x1", + "=> (iff (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x1", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] false).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x2", + "=> false.", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [false -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1973, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "c x1", + "=> (x1 exfalso@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal3).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]) -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]].", + "c x2", + "=> (x2 em@type exfalso@type x1 exfalso).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p2@type or_e@type p2 or_e).", + "c x1", + "=> (x1 goal19).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]); [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a x", + "=> (or (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]); [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> ('Q : prop) -> (iff 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'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 em@type p4@type em).", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 iff_er@type).", + "c em", + "=> (em goal3).", + "c iff_er", + "=> (iff_er iff_er@type p6@type@2 p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[(not x) -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [(not x) -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c iff_el", + "=> (iff_el iff_er@type p6@type@2 p6)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 434, + "actions": [ + "intro.", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not (not x))); (not (not x)).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "c not_e", + "=> (not_e not_e@type x0 not_e).", + "a or_e", + "=> [x -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not x) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a exfalso", + "=> .", + "intro.", + "a exfalso", + "=> .", + "c em", + "=> (em goal5).", + "c not_e", + "=> (not_e not_e@type x0 not_e).", + "c em", + "=> (em goal0@2@1).", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [(not x) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not (not x)) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a exfalso", + "=> .", + "c em", + "=> (em p0@type@2).", + "intro.", + "a or_e", + "=> [x -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not x) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]].", + "intro.", + "c x2", + "=> (x2 not_e@type x0 x2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 519, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [x -> (not (not x))]; [(not (not x)) -> x].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [x -> (not (not x))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [x -> (not (not x))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [x -> (not (not x))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [x -> (not (not x))]]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [x -> (not (not x))]]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [x -> (not (not x))]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal1).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]])]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em x).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 683, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff 'A (not (not 'A)))]].", + "intro.", + "intro.", + "a iff_i", + "=> [x0 -> (not (not x0))]; [(not (not x0)) -> x0].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [x0 -> (not (not x0))]].", + "intro.", + "c em", + "=> (em goal0).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x0 -> (not (not x0))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [x0 -> (not (not x0))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]])].", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]])] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal4).", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x0).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]])).", + "a x1", + "=> (and (and false (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]])).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not (not 'A)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> (iff 'A (not (not 'A)))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not (not 'A)))]); [('A : prop) -> (iff 'A (not (not 'A)))].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> (iff 'A (not (not 'A)))])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> (iff 'A (not (not 'A)))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not (not 'A)))]); [('A : prop) -> (iff 'A (not (not 'A)))].", + "a not_i", + "=> [[('A : prop) -> (iff 'A (not (not 'A)))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('A : prop) -> (iff 'A (not (not 'A)))] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('A : prop) -> (iff 'A (not (not 'A)))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 351, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [x -> (not (not x))]; [(not (not x)) -> x].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a 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-> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [(not false) -> [(iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x1", + "=> (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [false -> (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not false) -> (iff (not [('P : 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false)] false) (and (and [(not (not x)) -> x] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false)]) (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false)] false))))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false)] false) (and (and [(not (not x)) -> x] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false)]) (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false)] false))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))); (not (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))))]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))))]]).", + "c em", + "=> (em goal24).", + "a x0", 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false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7240, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not (not 'A)) -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> [(not (not 'A)) 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'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [(or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 300, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 546, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not x)) -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not (not x)) -> x]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> 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: prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a x1", + "=> (and (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a and_i", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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[(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x1", + "=> (and (and [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x1", + "=> (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or [[false -> ('P : prop) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[false -> ('P : prop) -> 'P] -> false] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]].", + "intro.", + "a x1", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) [('P : prop) -> (or 'P (not 'P))]); [(or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]) -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 395, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal10).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "intro.", + "c not_e", + "=> (not_e iff_i@type x2 iff_i).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "intro.", + "intro.", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]].", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 383, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])); (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false] -> false]; [(not [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false] -> false]; [(not [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5718, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x0", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "c x0", + "=> (x0 or_ir@type p2@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not false) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not false) -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 630, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('B : prop) -> [(not x) -> 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type and_el@type and_el).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5330, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))]))]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal14 not_e).", + "a x0", + "=> .", + "a x", + "=> (or (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]); [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]]; [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]].", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (or false (not false)) [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (and [('P : prop) -> (not 'P) -> 'P -> false] (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]])))).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2554, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", 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false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + 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prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6587, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x1", + "=> (x1 iff_i@type p@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 goal9 p@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]].", + "intro.", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 goal19 iff_i@type).", + "a x", + "=> (not (or [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false] (not [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]))).", + "c x1", + "=> (x1 p2@type em@type).", + "c x1", + "=> (x1 goal9 exfalso@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 449, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]].", + "a or_e", + "=> [x -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]; [(not x) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [x -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [x -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6765, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) [('P : prop) -> (or 'P (not 'P))]); [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]).", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2409, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type p2@type p2).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 461, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not (and x x0)) -> (or (not x) (not x0))]].", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P 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false])]].", + "a x0", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]))." + ] + }, + { + "mode": "sample", 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q 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: prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em p3@type@2).", + "a or_il", + "=> .", + "a x0", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x or_e@type p3 or_e).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + 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exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2161, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + 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'Q] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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-> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em goal1).", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em p@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : 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'Q]]) false); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [false -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) false)]; [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) false)].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); 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('P : prop) -> 'P]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "c x1", + "=> (x1 p1@type p4@type p1 p4).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2383, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false]].", + "c x1", + "=> (x1 not_e@type and_er@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 439, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [false -> ('P : prop) -> 'P]) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 321, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])].", + "a x", + "=> (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])])]).", + "a not_i", + "=> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])])] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]); [('A : prop) -> (not ['A -> (not 'A)]) -> 'A].", + "a not_i", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> 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false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x3", + "=> (x3 x1).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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"a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> false]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> false].", + "a x", + "=> [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]].", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 422, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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+ "=> (em goal9).", + "a or_e", + "=> [x -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not x) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [x -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [x -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [x -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [x -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]); [('A : prop) -> [(not 'A) -> 'A] -> 'A].", + "a not_i", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A])); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]))]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 551, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [[(not x) -> x] -> x]]; [(not false) -> [[(not x) -> x] -> x]].", 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em", + "=> (em p7@type@2).", + "c em", + "=> (em or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1001, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 iff_i).", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", 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-> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]].", + "intro.", + "c x1", + "=> (x1 not_e@type x0 x1).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]); [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + 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em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])); (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) [('P : prop) -> (not 'P) -> 'P -> false]); [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9315, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or [x -> 'B] ['B -> x])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or [x -> 'B] ['B -> x])]].", + "c x0", + "=> (x0 not_i@type or_il@type not_i or_il).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_il@type p1).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 exfalso@type and_er@type exfalso and_er).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_i@type p8@type not_i p8).", + "c p7", + "=> (p7 not_e@type and_i@type not_e p7).", + "c x1", + "=> (x1 and_i@type and_i@type x1 x1).", + "c x0", + "=> (x0 not_e@type and_er@type not_e and_er).", + "a exfalso", + "=> false.", + "c p7", + "=> (p7 and_er@type p5@type and_er p5).", + "c em", + "=> (em goal4@1).", + "c x1", + "=> (x1 iff_el@type iff_el@type iff_el iff_el).", + "c x1", + "=> (x1 p14@type p1@type p14 p1).", + "c x0", + "=> (x0 p14@type and_i@type p14 p7).", + "c p7", + "=> (p7 p11@type not_i@type p11 not_i).", + "c and_er", + "=> (and_er and_i@type or_il@type p2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2419, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x", + "=> (x or_e@type p1@type p1).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))))).", + "c x", + "=> (x p4@type@2 or_il@type or_il).", + "a not_i", + "=> [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))) -> false].", + "intro.", + "c x", + "=> (x goal11 em@type em).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "intro.", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 610, + "actions": [ + "intro.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> (or [x -> 'B] ['B -> x])]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]].", + "a exfalso", + "=> false.", + "a x0", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]])).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] -> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false)]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]) -> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false)].", + "intro.", + "c x1", + "=> (x1 and_er).", + "c x1", + "=> (x1 x0).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] -> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false)]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]) -> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] -> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false)]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] -> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false)]].", + "intro.", + "a x0", + "=> (and (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] -> (and (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]])) false) false)]).", + "c p7", + "=> (p7 p0@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 549, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]); [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])])]].", + "intro.", + "intro.", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false].", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]].", + "c em", + "=> (em p10@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 21, + "evals_used": 119, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [false -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not false) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> .", + "intro.", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 564, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "c em", 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-> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_er@type or_ir@type iff_er or_ir).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) false).", + "c x0", + "=> (x0 iff_er@type or_ir@type p4).", + "c em", + "=> (em goal14).", + "a and_i", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false); false.", + "c and_el", + "=> (and_el iff_er@type or_ir@type p4).", + "c em", + "=> (em p6@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4992, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c x0", + "=> (x0 p6@type p1@type p6).", + "c x0", + "=> (x0 exfalso@type p4@type@2 exfalso).", + "c x0", + "=> (x0 p7@type em@type p7).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 iff_el@type goal5 iff_el).", + "c x0", + "=> (x0 p3@type not_e@type p3).", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c em", + "=> (em p7@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2333, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> 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60, + "evals_used": 435, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] false).", + "a and_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; false.", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6404, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [[('P : prop) -> (or 'P (not 'P))] -> false])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]])); (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]) -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3858, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p0@type p0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> false].", + "a or_ir", + "=> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type p@type p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]].", + "intro.", + "intro.", + "a or_e" + ] + } + ], + "problem": "extrinsic_L4_14" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 30991, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_i@type and_el@type x0 and_el).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 492, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c not_e", + "=> (not_e not_e@type x0 not_e).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 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false] -> (not 'P)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1998, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e and_er@type x1 and_er).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, 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(not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])); (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 p3@type@2).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type@2).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]].", + "intro.", + "c em", + "=> (em or_e@type).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 392, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [false -> false]].", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em goal3).", + "c em", + "=> (em and_el@type).", + "intro.", + "c x0", + "=> (x0 goal em@type em).", + "c em" + ] + } + ], + "problem": "extrinsic_L5_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 24222, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : 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'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> (or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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-> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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'B))) 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 not_i@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x0", + "=> (or (iff (and (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(iff (and (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)])) -> (or (iff (and (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not (or [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]))) -> (or (iff (and (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not x) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not x); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [x -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 583, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + 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false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [false -> ('P : prop) -> 'P])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [false -> ('P : prop) -> 'P])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 519, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c em", + "=> (em em@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c em", + "=> (em goal9).", + "intro.", + "intro.", + 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['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "intro.", + "c em", + "=> (em exfalso@type).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 512, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + 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+ "=> (em iff_er@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) 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prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])); (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 466, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : 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-> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "c em", + "=> (em goal12).", + "c x1", + "=> (x1 p8@type).", + "c em", + 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false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : 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'P]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [false -> ('P : prop) -> 'P]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [false -> ('P : prop) -> 'P]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 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(and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) false)))) (and (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) false)))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) false) false).", + "c em", + "=> (em goal12).", + "a and_i", + "=> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) false); false.", + "a and_i", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3990, 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + 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x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]]; [false -> [false -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10529, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em goal4@2).", + "c x1", + "=> (x1 exfalso@type and_er@type exfalso and_er).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_i@type p6@type p4 p6).", + "c p7", + "=> (p7 not_e@type and_i@type not_e p7).", + "c x1", + "=> (x1 and_i@type and_i@type x1 x1).", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "a exfalso", + "=> false.", + "c p7", + "=> (p7 and_er@type p5@type and_er 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x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 p1@type and_i@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type and_er@type and_er).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 501, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em or_il@type).", + "a or_ir", + "=> (iff x (not x0)).", + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 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-> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "c em", + "=> (em x0).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [x0 -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not x0) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c em", + "=> (em p1@type).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em goal0@1).", + "c em", + "=> (em p5@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a x4" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em goal6).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em or_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2399, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 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'R] -> 'R] -> false])].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 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-> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2232, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A 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"=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [false -> [false -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3283, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type and_er@type and_er).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type and_er@type and_er).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1861, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c x0", + "=> (x0 goal15 false).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]].", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]]]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]]].", + "intro.", + "c iff_el", + "=> (iff_el p6@type@1 p6@type@2 p6).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 392, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : 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prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ['P -> false] -> (not 'P)])); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(or false [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]) -> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (and (or x (not x2)) (or (not x) x2))); (and (or x (not x2)) (or (not x) x2)).", + "c em", + "=> (em x).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not (not x2))); (not (not x2)).", + "c em", + "=> (em x2).", + "c em", + "=> (em goal5).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em exfalso@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1356, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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-> [[false -> ('P : prop) -> 'P] -> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "a x1", + "=> false.", + "a x1", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3353, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a x3", + "=> (not (or [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false] (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]))).", + "c em", + "=> (em p2@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))).", + "a and_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 424, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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-> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1459, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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-> false]); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> ['B -> 'C] -> ['C -> x] -> (iff x 'B)]] (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P])))); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> ['B -> 'C] -> ['C -> x] -> (iff x 'B)]] -> false]; [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> ['B -> 'C] -> ['C -> x] -> (iff x 'B)]] (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))))]; [[('P : prop) -> (or 'P (not 'P))] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> ['B -> 'C] -> ['C -> x] -> (iff x 'B)]] (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))))].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal9)." + ] + 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-> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))); (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]].", + "intro.", + "c em", + "=> (em p5@type).", + "c em" + ] 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + 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-> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]]].", + "c x2", + "=> (x2 em@type and_i@type em and_i).", + "c x2", + "=> (x2 iff_i@type iff_el@type iff_i iff_el).", + "c x2", + "=> (x2 p2@type or_ir@type p2 or_ir).", + "c x1", + "=> (x1 p4@type em@type p4).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 36247, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) 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(or 'A 'C) (or (not 'A) 'B)))]) -> false].", + "c x0", + "=> (x0 em@type or_il@type p1@type@2).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "intro.", + "c x", + "=> (x em@type 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false])))]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])))].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[false -> ('P : prop) -> 'P] -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))]; [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> false]; [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 547, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q 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false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a p4", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] -> (or (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P 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(not (or (not x0) (not (not x0))))]]].", + "a or_e", + "=> [(not x0) -> [[x0 -> false] -> [[x0 -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))]]]]; [(not (not x0)) -> [[x0 -> false] -> [[x0 -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))]]]].", + "c x2", + "=> (x2 goal11 p1@type p1).", + "c x2", + "=> (x2 p0@type@2 p3@type p3).", + "c x2", + "=> (x2 goal16 or_e@type x1).", + "a x1", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))] -> [(not x0) -> [[x0 -> false] -> [[x0 -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))]]]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not x0) -> [[x0 -> false] -> [[x0 -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))]]]]].", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (not 'P) -> 'P -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not x0) (not (not x0))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 343, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a 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-> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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: prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))])).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 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prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [(not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 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or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not 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-> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]).", + "intro.", + "a or_e", + "=> [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> false]; [(not (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])))) -> false].", + "a x", + "=> (and [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (and [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> (and [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", 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not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7372, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "c x0", + "=> (x0 or_ir@type p2@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + 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+ "a exfalso", + "=> false.", + "a x1", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal11).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3370, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) 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(x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c x0", + "=> (x0 goal11 em@type em).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 goal9 or_ir@type x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "intro.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 347, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c not_e", + "=> (not_e and_er@type x and_er).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e and_er@type x and_er).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c not_e", + "=> (not_e not_e@type x0 not_e).", + "c not_e", + "=> (not_e and_er@type x and_er).", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal13).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e and_er@type x and_er).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 512, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]]; [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em goal).", + "a x", + "=> (iff (not [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a iff_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])))); (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2402, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "c x", + "=> (x iff_i@type not_e@type not_e).", + "c x", + "=> (x not_i@type p@type p).", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em goal3).", + "c em", + "=> (em and_el@type).", + "intro.", + "c x", + "=> (x iff_er@type p5@type p5).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a x0", + "=> [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> false]." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..fb2709c313b454e1e354ea45f8667a4efafeb34e --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,827 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_3 (traces=17 evals=21053) +[ ] - extrinsic_L0_4 (traces=17 evals=24119) +[ ] - extrinsic_L0_2 (traces=17 evals=28158) +[ ] - extrinsic_L0_1 (traces=17 evals=23163) +[ ] - extrinsic_L0_6 (traces=13 evals=20141) +[ ] - extrinsic_L0_5 (traces=7 evals=13001) +[ ] - extrinsic_L0_7 (traces=17 evals=15057) +[OK ] - extrinsic_L0_10 (traces=5 evals=12173) +[ ] - extrinsic_L0_8 (traces=17 evals=17868) + +thread '' (744561) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)] (x0 [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] or_e iff_el)): parameter type (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)]) and value type (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (744561) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)] (x0 [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] or_e iff_el)): parameter type (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)]) and value type (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) did not unify. +[ ] - extrinsic_L0_9 (traces=17 evals=17132) + +thread '' (744558) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ['P -> false] -> (not 'P)] (x0 [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] not_i iff_er)): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ['P -> false] -> (not 'P)]) and value type (and [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_12 (traces=13 evals=29302) +[ ] - extrinsic_L0_11 (traces=7 evals=19927) +[ ] - extrinsic_L0_13 (traces=15 evals=28101) +[ ] - extrinsic_L0_14 (traces=4 evals=20606) +[ ] - extrinsic_L1_1 (traces=11 evals=25234) + +thread '' (744560) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (744560) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744554) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_2 (traces=13 evals=29667) +[ ] - extrinsic_L1_4 (traces=17 evals=26726) +[ ] - extrinsic_L2_2 (traces=17 evals=23676) +[ ] - extrinsic_L1_3 (traces=16 evals=35411) +[ ] - extrinsic_L2_1 (traces=17 evals=29100) +[ ] - extrinsic_L2_7 (traces=17 evals=12131) +[ ] - extrinsic_L2_3 (traces=12 evals=14984) + +thread '' (744554) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_4 (traces=13 evals=23928) +[ ] - extrinsic_L2_5 (traces=14 evals=27990) +[ ] - extrinsic_L2_6 (traces=13 evals=26608) +[ ] - extrinsic_L2_8 (traces=17 evals=15136) + +thread '' (744560) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_9 (traces=17 evals=20292) +[ ] - extrinsic_L2_10 (traces=17 evals=16061) +[ ] - extrinsic_L2_12 (traces=17 evals=16690) + +thread '' (744558) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_11 (traces=14 evals=29501) +[ ] - extrinsic_L3_1 (traces=17 evals=22401) +[ ] - extrinsic_L2_13 (traces=11 evals=11950) +[ ] - extrinsic_L3_4 (traces=17 evals=16294) + +thread '' (744560) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744557) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (744560) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744557) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_2 (traces=15 evals=26435) +[ ] - extrinsic_L3_3 (traces=17 evals=24133) + +thread '' (744559) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_5 (traces=11 evals=18558) + +thread '' (744559) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744560) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744560) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_6 (traces=11 evals=23067) +[ ] - extrinsic_L3_7 (traces=14 evals=17225) +[ ] - extrinsic_L3_8 (traces=17 evals=28746) +[ ] - extrinsic_L3_9 (traces=17 evals=25356) +[ ] - extrinsic_L3_10 (traces=17 evals=31367) +[ ] - extrinsic_L3_11 (traces=17 evals=14297) +[ ] - extrinsic_L3_12 (traces=17 evals=20196) +[ ] - extrinsic_L3_13 (traces=14 evals=24628) +[ ] - extrinsic_L3_14 (traces=16 evals=16837) +[ ] - extrinsic_L3_15 (traces=11 evals=21989) +[ ] - extrinsic_L3_16 (traces=17 evals=29321) +[ ] - extrinsic_L3_18 (traces=17 evals=25147) +[ ] - extrinsic_L3_17 (traces=14 evals=27679) +[ ] - extrinsic_L3_19 (traces=11 evals=7599) +[ ] - extrinsic_L3_20 (traces=13 evals=22588) +[ ] - extrinsic_L3_22 (traces=17 evals=17712) +[ ] - extrinsic_L3_21 (traces=6 evals=2767) +[ ] - extrinsic_L3_23 (traces=15 evals=24355) +[ ] - extrinsic_L3_24 (traces=17 evals=25969) +[ ] - extrinsic_L3_25 (traces=17 evals=21241) +[ ] - extrinsic_L3_26 (traces=11 evals=6228) +[ ] - extrinsic_L3_27 (traces=14 evals=22217) +[ ] - extrinsic_L3_28 (traces=8 evals=13633) +[ ] - extrinsic_L3_29 (traces=8 evals=15179) +[ ] - extrinsic_L4_1 (traces=17 evals=27278) +[ ] - extrinsic_L4_3 (traces=17 evals=13363) +[ ] - extrinsic_L4_2 (traces=17 evals=30759) +[ ] - extrinsic_L4_4 (traces=17 evals=23169) +[ ] - extrinsic_L4_5 (traces=15 evals=28417) + +thread '' (744558) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_6 (traces=13 evals=18387) +[ ] - extrinsic_L4_7 (traces=17 evals=33037) + +thread '' (744559) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744559) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744559) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_8 (traces=13 evals=20950) +[ ] - extrinsic_L4_9 (traces=13 evals=18139) +[ ] - extrinsic_L4_10 (traces=11 evals=28504) + +thread '' (744554) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_11 (traces=13 evals=26366) +[ ] - extrinsic_L4_12 (traces=15 evals=22012) +[ ] - extrinsic_L4_13 (traces=17 evals=23191) +[ ] - extrinsic_L4_14 (traces=14 evals=27286) +[ ] - extrinsic_L5_1 (traces=17 evals=30991) +[ ] - extrinsic_L5_2 (traces=17 evals=24222) +[ ] - extrinsic_L5_3 (traces=17 evals=15322) +[ ] - extrinsic_L5_5 (traces=17 evals=24010) +[ ] - extrinsic_L5_4 (traces=17 evals=20723) +[ ] - extrinsic_L5_8 (traces=17 evals=18620) +[ ] - extrinsic_L5_7 (traces=17 evals=19938) +[ ] - extrinsic_L5_6 (traces=17 evals=35188) +[ ] - extrinsic_L5_10 (traces=17 evals=18503) +[ ] - extrinsic_L5_9 (traces=11 evals=18193) +[ ] - extrinsic_L5_11 (traces=8 evals=64602) +[ ] - extrinsic_L6_1 (traces=11 evals=26892) +[ ] - extrinsic_L6_2 (traces=11 evals=47136) +[ ] - extrinsic_L6_5 (traces=13 evals=26481) +[ ] - extrinsic_L6_4 (traces=8 evals=19284) +[ ] - extrinsic_L6_3 (traces=6 evals=53270) +[ ] - extrinsic_L6_6 (traces=1 evals=214) +[ ] - extrinsic_L6_7 (traces=17 evals=26892) +[ ] - extrinsic_L6_9 (traces=17 evals=22413) +[ ] - extrinsic_L6_8 (traces=3 evals=56056) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> 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(and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] 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[('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not 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(iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 1/94 in 9116.4s diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..7aa32ea7b58b9819a5c27afc412f2dd52ef2f9cf --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log @@ -0,0 +1,218 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_4 (traces=17 evals=23155) +[ ] - extrinsic_L0_5 (traces=17 evals=28348) +[OK ] g extrinsic_L0_8 (traces=1 evals=15) +[ ] - extrinsic_L0_3 (traces=17 evals=28393) +[ ] - extrinsic_L0_2 (traces=17 evals=23558) +[OK ] - extrinsic_L0_10 (traces=5 evals=5212) +[ ] - extrinsic_L0_1 (traces=15 evals=20974) +[ ] - extrinsic_L0_6 (traces=7 evals=18090) + +thread '' (924253) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)] (x0 [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] or_e iff_el)): parameter type (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)]) and value type (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (924253) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)] (x0 [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] or_e iff_el)): parameter type (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)]) and value type (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) did not unify. +[ ] - extrinsic_L0_7 (traces=17 evals=22545) +[ ] - extrinsic_L0_9 (traces=17 evals=22341) +[ ] - extrinsic_L0_13 (traces=17 evals=23041) +[ ] - extrinsic_L0_11 (traces=17 evals=32451) +[ ] - extrinsic_L0_12 (traces=17 evals=28679) +[ ] - extrinsic_L0_14 (traces=5 evals=13608) + +thread '' (924246) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_1 (traces=17 evals=26875) +[ ] - extrinsic_L1_2 (traces=17 evals=29230) +[ ] - extrinsic_L1_3 (traces=17 evals=29832) +[ ] - extrinsic_L1_4 (traces=17 evals=31861) +[ ] - extrinsic_L2_1 (traces=17 evals=27431) +[ ] - extrinsic_L2_2 (traces=17 evals=28764) +[ ] - extrinsic_L2_4 (traces=17 evals=14329) +[ ] - extrinsic_L2_3 (traces=15 evals=23037) +[ ] - extrinsic_L2_6 (traces=17 evals=26885) +[ ] - extrinsic_L2_5 (traces=11 evals=14412) +[ ] - extrinsic_L2_8 (traces=17 evals=18367) +[ ] - extrinsic_L2_7 (traces=14 evals=17103) +[ ] - extrinsic_L2_9 (traces=14 evals=29705) +[ ] - extrinsic_L2_10 (traces=15 evals=29551) +[ ] - extrinsic_L2_12 (traces=17 evals=22008) +[ ] - extrinsic_L3_1 (traces=17 evals=26728) +[ ] - extrinsic_L2_11 (traces=13 evals=26370) +[ ] - extrinsic_L2_13 (traces=9 evals=12173) +[ ] - extrinsic_L3_2 (traces=12 evals=12569) +[ ] - extrinsic_L3_3 (traces=6 evals=16980) +[ ] - extrinsic_L3_6 (traces=17 evals=11451) +[ ] - extrinsic_L3_4 (traces=13 evals=28124) +[ ] - extrinsic_L3_5 (traces=13 evals=17425) +[ ] - extrinsic_L3_7 (traces=17 evals=22739) +[ ] - extrinsic_L3_8 (traces=17 evals=19219) +[ ] - extrinsic_L3_9 (traces=17 evals=30355) +[ ] - extrinsic_L3_11 (traces=17 evals=17216) +[ ] - extrinsic_L3_10 (traces=17 evals=28814) +[ ] - extrinsic_L3_12 (traces=17 evals=20673) +[ ] - extrinsic_L3_13 (traces=13 evals=31594) +[ ] - extrinsic_L3_14 (traces=17 evals=22505) + +thread '' (924246) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_18 (traces=17 evals=20429) +[ ] - extrinsic_L3_15 (traces=6 evals=26336) +[ ] - extrinsic_L3_16 (traces=14 evals=34861) +[ ] - extrinsic_L3_17 (traces=13 evals=33041) +[ ] - extrinsic_L3_19 (traces=17 evals=28739) +[ ] - extrinsic_L3_20 (traces=17 evals=22939) +[ ] - extrinsic_L3_23 (traces=17 evals=18999) +[ ] - extrinsic_L3_24 (traces=17 evals=25875) +[ ] - extrinsic_L3_21 (traces=11 evals=22170) +[ ] - extrinsic_L3_22 (traces=15 evals=18561) +[ ] - extrinsic_L3_25 (traces=17 evals=23845) +[ ] - extrinsic_L3_26 (traces=10 evals=11257) +[ ] - extrinsic_L3_29 (traces=17 evals=17710) +[ ] - extrinsic_L3_27 (traces=11 evals=17496) +[ ] - extrinsic_L3_28 (traces=7 evals=18106) +[ ] - extrinsic_L4_1 (traces=14 evals=24344) +[ ] - extrinsic_L4_3 (traces=17 evals=16554) +[ ] - extrinsic_L4_2 (traces=17 evals=24130) + +thread '' (924250) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (924250) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924250) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_4 (traces=16 evals=20779) +[ ] - extrinsic_L4_5 (traces=13 evals=26088) +[ ] - extrinsic_L4_6 (traces=11 evals=19343) +[ ] - extrinsic_L4_7 (traces=11 evals=27689) +[ ] - extrinsic_L4_8 (traces=13 evals=14955) +[ ] - extrinsic_L4_10 (traces=17 evals=18043) +[ ] - extrinsic_L4_9 (traces=16 evals=20268) +[ ] - extrinsic_L4_13 (traces=17 evals=22809) +[ ] - extrinsic_L4_11 (traces=17 evals=29398) +[ ] - extrinsic_L4_14 (traces=17 evals=21910) +[ ] - extrinsic_L4_12 (traces=15 evals=20439) +[ ] - extrinsic_L5_1 (traces=17 evals=25854) + +thread '' (924252) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L5_6 (traces=17 evals=23350) +[ ] - extrinsic_L5_2 (traces=3 evals=19561) +[ ] - extrinsic_L5_3 (traces=12 evals=24236) +[ ] - extrinsic_L5_4 (traces=9 evals=14453) +[ ] - extrinsic_L5_5 (traces=11 evals=30233) +[ ] - extrinsic_L5_7 (traces=17 evals=19676) +[ ] - extrinsic_L5_8 (traces=17 evals=18994) + +thread '' (924253) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924253) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924253) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=13 evals=30688) +[ ] - extrinsic_L5_10 (traces=7 evals=22307) +[ ] - extrinsic_L5_11 (traces=15 evals=23897) +[ ] - extrinsic_L6_1 (traces=14 evals=9991) +[ ] - extrinsic_L6_2 (traces=17 evals=24958) diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..4fcb890a03703ddbe29efbb64641d87f8848dce2 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 50 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s44/train.log b/experiments/learnability/train_policy_only/minimo_0pt/s44/train.log new file mode 100644 index 0000000000000000000000000000000000000000..42d7e04f1298cfe98d78b59cfaf3e512c67b089b --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s44/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_053016-rnijnopm +[2026-06-28T05:30:13.331795] Seeded RNGs with seed=44 +[2026-06-28T05:30:13.332053] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-28T05:30:16.621237] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json + 1567 training examples loaded. + +============================================================ +[2026-06-28T05:30:16.623555] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 1567 -> 1567 unique examples + Epoch 1/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 50 total steps, 1567 unique examples (batch_size=64) +[2026-06-28T05:30:27.455727] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:30:27.462978] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s44/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 50} diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/summary.json b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..8068db743ceb9551448868a7a1d8dc554308a5de --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + 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null, + "problem": "extrinsic_L4_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26266, + "max_open": 22267, + "solution_actions": null, + "problem": "extrinsic_L4_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26760, + "max_open": 22761, + "solution_actions": null, + "problem": "extrinsic_L4_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25355, + "max_open": 21356, + "solution_actions": null, + "problem": "extrinsic_L4_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26259, + "max_open": 22260, + "solution_actions": null, + "problem": "extrinsic_L4_11" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 1335, + "evals_used": 7423, + "max_open": 6086, + "solution_actions": [ + "intro.", + "intro.", + "c em", + "=> (em x).", + "a or_e", + "=> [x -> x].", + "intro." + ], + "problem": "extrinsic_L4_12" + 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"evals_used": 26511, + "max_open": 22512, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31379, + "max_open": 27380, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25980, + "max_open": 21981, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31377, + "max_open": 27378, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31288, + "max_open": 27289, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31112, + "max_open": 27113, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31009, + "max_open": 27010, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26062, + "max_open": 22063, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25975, + "max_open": 21976, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31329, + "max_open": 27330, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31130, + "max_open": 27131, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..81d36b6e27d8f7db23307a0453355fafab414637 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=5 evals=25 maxopen=19) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_3 (solved pops=61 evals=368 maxopen=308) +[OK ] extrinsic_L0_5 (solved pops=56 evals=368 maxopen=313) +[OK ] extrinsic_L0_6 (solved pops=57 evals=353 maxopen=297) +[OK ] extrinsic_L0_10 (solved pops=7 evals=41 maxopen=35) +[OK ] extrinsic_L0_7 (solved pops=55 evals=353 maxopen=299) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=20 evals=152 maxopen=133) +[OK ] extrinsic_L0_8 (solved pops=57 evals=358 maxopen=302) +[OK ] extrinsic_L0_9 (solved pops=55 evals=367 maxopen=297) +[OK ] extrinsic_L0_4 (solved pops=210 evals=1122 maxopen=913) +[OK ] extrinsic_L1_4 (solved pops=15 evals=100 maxopen=84) +[OK ] extrinsic_L0_11 (solved pops=208 evals=1124 maxopen=917) +[OK ] extrinsic_L1_1 (solved pops=222 evals=1219 maxopen=980) +[OK ] extrinsic_L1_3 (solved pops=457 evals=2427 maxopen=1971) +[OK ] extrinsic_L1_2 (solved pops=457 evals=2430 maxopen=1974) +[OK ] extrinsic_L2_1 (solved pops=1257 evals=6862 maxopen=5606) +[OK ] extrinsic_L2_6 (solved pops=1618 evals=9341 maxopen=7724) +[OK ] extrinsic_L2_7 (solved pops=984 evals=5440 maxopen=4457) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26048 maxopen=22049) +[OK ] extrinsic_L0_14 (solved pops=3978 evals=26098 maxopen=22121) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25927 maxopen=21928) +[OK ] extrinsic_L2_11 (solved pops=22 evals=145 maxopen=122) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25922 maxopen=21923) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25789 maxopen=21790) +[OK ] extrinsic_L2_9 (solved pops=998 evals=5585 maxopen=4588) +[OK ] extrinsic_L2_12 (solved pops=1377 evals=7853 maxopen=6477) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26004 maxopen=22005) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26412 maxopen=22413) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25810 maxopen=21811) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25925 maxopen=21926) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25845 maxopen=21846) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25893 maxopen=21894) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26119 maxopen=22120) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26071 maxopen=22072) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25790 maxopen=21791) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25893 maxopen=21894) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25982 maxopen=21983) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26179 maxopen=22180) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25929 maxopen=21930) +[ ] extrinsic_L3_11 (budget pops=4000 evals=26227 maxopen=22228) +[OK ] extrinsic_L3_14 (solved pops=3220 evals=19714 maxopen=16495) +[OK ] extrinsic_L3_13 (solved pops=3545 evals=22847 maxopen=19303) +[ ] extrinsic_L3_12 (budget pops=4000 evals=26228 maxopen=22229) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26013 maxopen=22014) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26030 maxopen=22031) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25726 maxopen=21727) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25602 maxopen=21603) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25983 maxopen=21984) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26098 maxopen=22099) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26128 maxopen=22129) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25882 maxopen=21883) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26248 maxopen=22249) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26148 maxopen=22149) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26835 maxopen=22836) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25911 maxopen=21912) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26301 maxopen=22302) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25794 maxopen=21795) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26048 maxopen=22049) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26861 maxopen=22862) +[ ] extrinsic_L4_2 (budget pops=4000 evals=25875 maxopen=21876) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26054 maxopen=22055) +[ ] extrinsic_L4_4 (budget pops=4000 evals=26006 maxopen=22007) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26083 maxopen=22084) +[ ] extrinsic_L4_6 (budget pops=4000 evals=26007 maxopen=22008) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26731 maxopen=22732) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26266 maxopen=22267) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26760 maxopen=22761) +[OK ] extrinsic_L4_12 (solved pops=1335 evals=7423 maxopen=6086) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25355 maxopen=21356) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26259 maxopen=22260) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25911 maxopen=21912) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26299 maxopen=22300) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25806 maxopen=21807) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26186 maxopen=22187) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26256 maxopen=22257) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25985 maxopen=21986) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26576 maxopen=22577) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26089 maxopen=22090) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26502 maxopen=22503) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26409 maxopen=22410) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26259 maxopen=22260) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26511 maxopen=22512) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31379 maxopen=27380) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25980 maxopen=21981) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31377 maxopen=27378) +[ ] extrinsic_L6_4 (budget pops=4000 evals=31112 maxopen=27113) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31288 maxopen=27289) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31009 maxopen=27010) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26062 maxopen=22063) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25975 maxopen=21976) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31130 maxopen=27131) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31329 maxopen=27330) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) 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b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..bb5d7582b2e38ca4e55469f1a394bccb78a4e394 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> 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[('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_6 (solved pops=51 evals=316 maxopen=266) +[OK ] extrinsic_L0_5 (solved pops=53 evals=321 maxopen=269) +[OK ] extrinsic_L0_2 (solved pops=53 evals=346 maxopen=294) +[OK ] extrinsic_L0_7 (solved pops=53 evals=348 maxopen=296) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_3 (solved pops=77 evals=447 maxopen=371) +[OK ] extrinsic_L0_13 (solved pops=21 evals=167 maxopen=147) +[OK ] extrinsic_L0_9 (solved pops=49 evals=328 maxopen=264) +[OK ] extrinsic_L0_8 (solved pops=51 evals=343 maxopen=293) +[OK ] extrinsic_L0_4 (solved pops=224 evals=1210 maxopen=987) +[OK ] extrinsic_L1_4 (solved pops=15 evals=101 maxopen=85) +[OK ] extrinsic_L0_11 (solved pops=222 evals=1183 maxopen=962) +[OK ] extrinsic_L1_1 (solved pops=218 evals=1185 maxopen=950) +[OK ] extrinsic_L1_2 (solved pops=482 evals=2650 maxopen=2169) +[OK ] extrinsic_L1_3 (solved pops=482 evals=2647 maxopen=2166) +[OK ] extrinsic_L2_1 (solved pops=1230 evals=6819 maxopen=5590) +[OK ] extrinsic_L2_6 (solved pops=1722 evals=10150 maxopen=8429) +[OK ] extrinsic_L2_7 (solved pops=989 evals=5596 maxopen=4608) +[OK ] extrinsic_L0_14 (solved pops=3848 evals=25445 maxopen=21598) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25962 maxopen=21963) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25911 maxopen=21912) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25892 maxopen=21893) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25690 maxopen=21691) +[OK ] extrinsic_L2_9 (solved pops=959 evals=5412 maxopen=4454) +[OK ] extrinsic_L2_12 (solved pops=1215 evals=6763 maxopen=5549) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26318 maxopen=22319) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26201 maxopen=22202) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25620 maxopen=21621) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25909 maxopen=21910) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25627 maxopen=21628) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25661 maxopen=21662) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26000 maxopen=22001) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25988 maxopen=21989) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25690 maxopen=21691) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25884 maxopen=21885) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25962 maxopen=21963) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26065 maxopen=22066) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25927 maxopen=21928) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25880 maxopen=21881) +[OK ] extrinsic_L3_14 (solved pops=3137 evals=19390 maxopen=16254) +[OK ] extrinsic_L3_13 (solved pops=3543 evals=22849 maxopen=19307) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25884 maxopen=21885) +[ ] extrinsic_L3_15 (budget pops=4000 evals=25792 maxopen=21793) +[ ] extrinsic_L3_16 (budget pops=4000 evals=25797 maxopen=21798) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25597 maxopen=21598) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25608 maxopen=21609) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25863 maxopen=21864) +[ ] extrinsic_L3_20 (budget pops=4000 evals=25968 maxopen=21969) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25943 maxopen=21944) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25823 maxopen=21824) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26136 maxopen=22137) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26188 maxopen=22189) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26878 maxopen=22879) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25990 maxopen=21991) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26086 maxopen=22087) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25845 maxopen=21846) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26048 maxopen=22049) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26809 maxopen=22810) +[ ] extrinsic_L4_3 (budget pops=4000 evals=25686 maxopen=21687) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26997 maxopen=22998) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25915 maxopen=21916) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26090 maxopen=22091) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25884 maxopen=21885) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26726 maxopen=22727) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26361 maxopen=22362) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25812 maxopen=21813) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25757 maxopen=21758) +[OK ] extrinsic_L4_12 (solved pops=1340 evals=7703 maxopen=6361) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26313 maxopen=22314) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25908 maxopen=21909) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26214 maxopen=22215) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26018 maxopen=22019) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26138 maxopen=22139) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26212 maxopen=22213) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25998 maxopen=21999) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26466 maxopen=22467) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26129 maxopen=22130) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26231 maxopen=22232) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26305 maxopen=22306) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26668 maxopen=22669) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26579 maxopen=22580) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31224 maxopen=27225) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25735 maxopen=21736) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31060 maxopen=27061) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31020 maxopen=27021) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30856 maxopen=26857) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30895 maxopen=26896) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25791 maxopen=21792) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25582 maxopen=21583) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31291 maxopen=27292) +[ ] extrinsic_L6_9 (budget pops=4000 evals=30863 maxopen=26864) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) 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'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] 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[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 27/94 in 2751.2s diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..86b907b72a212d6d6b408f8e8e0ff6fb032776d5 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json @@ -0,0 +1,92739 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/epoch_2.pt", + "problemset": "extrinsic-95", + "n_samples": 16, + "max_depth": 60, + "temperature": 1.0, + "greedy_first": true, + "seed": 0, + "workers": 6, + "timeout": 600.0, + "max_actions": 0, + "num_problems": 94, + "num_solved": 1, + "elapsed_sec": 9151.3720870018, + "results": [ + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19371, + "solution_actions": null, + 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+ "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (iff false (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (iff false (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2336, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> false]]].", + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 or_il@type not_e@type or_il not_e).", + "c em", + "=> (em p1@type@2).", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal6).", + "c x2", + "=> (x2 p0@type p6@type p0 p6).", + "c x2", + "=> (x2 p7@type iff_el@type p7 iff_el).", + "c em", + "=> (em or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7240, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal7).", + "intro.", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type).", + "intro.", + "a x0", + "=> (or [[[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_ir", + "=> .", + "a x0", + "=> (or (not (not [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 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false]]]))]; [[[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]] -> (not (not [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]]))].", + "c em", + "=> (em and_el@type).", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]])].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[[[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]] -> false] -> false].", + "a or_ir", + "=> [[[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 653, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (and false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (and false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false).", + "a or_e", + "=> [[('P : 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 511, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a iff_i", + "=> [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 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-> 'Q -> (and 'P 'Q)]) -> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]]]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]) -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + 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prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]).", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false] (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]); [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x goal or_e@type and_el).", + "c x", + "=> (x iff_i@type or_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2189, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x goal goal16 and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not false))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not false))).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not false)))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not false)))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9747, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and x 'B) -> x]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type p@type p0 p).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type p4 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> 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prop) -> (and 'A 'B) -> 'B]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "c x2", + "=> (x2 and_er@type and_el@type x1 and_el).", + "c x1", + "=> (x1 goal and_el@type p1).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 iff_el@type p1@type iff_el p1).", + "a p2", + "=> (and false x0).", + "a x2", + "=> false; x0.", + "c x2", + "=> (x2 and_er@type and_i@type x1 and_i).", + "c x1", + "=> (x1 and_er@type and_i@type p4).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c and_el", + "=> (and_el and_er@type and_el@type p1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c p7", + "=> (p7 goal and_i@type p4).", + "c p8", + "=> (p8 iff_i@type em@type iff_i em).", + "c p8", + "=> (p8 p1@type and_i@type p1 p8).", + "c p5", + "=> (p5 p4@type iff_i@type p4 iff_i).", + "a p2", + "=> (and [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])); (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> (not (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> (not (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> 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prop) -> (and 'A 'B) -> 'B]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))].", + "intro.", + "c x", + "=> (x goal or_e@type and_er).", + "c x", + "=> (x iff_i@type or_ir@type iff_i).", + "a exfalso", 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'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7123, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]]]; [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]]].", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]); [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p1@type not_e p1).", + "c and_el", + "=> (and_el not_e@type p1@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso and_er).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3319, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p@type p).", + "a not_e", + "=> (not (not (not x))); (not (not x)).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not (not x)))]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (not (not x)))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 goal12 not_i@type not_i).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 p1@type or_e@type or_e).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em iff_el@type).", + "c x0", + "=> (x0 goal7 p5@type p5).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a or_e", + "=> [(not x) -> false]; [(not (not x)) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 639, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type@2).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [(not [('P : 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false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (not (or [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])))).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false]; (not (or [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]))).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not (or [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]))) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1423, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7442, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> (not 'P) -> 'P -> false]); [false -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p0@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type p3@type@2 not_e).", + "c x0", + "=> (x0 exfalso@type or_ir@type exfalso).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P]); [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [[false -> ('P : prop) -> 'P] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "c x0", + "=> (x0 or_e@type and_i@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 361, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a not_e", + "=> (not x); x." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11059, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> 'B -> (and x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c and_el", + "=> (and_el not_e@type p2@type p3).", + "c x0", + "=> (x0 p0@type exfalso@type p0 exfalso).", + "c x1", + "=> (x1 iff_i@type or_ir@type iff_i or_ir).", + "c and_el", + "=> (and_el p0@type exfalso@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type goal exfalso x0).", + "c x1", + "=> (x1 exfalso@type p3@type exfalso p3).", + "c x0", + "=> (x0 and_i@type and_er@type x0 and_er).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type goal or_ir x0).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x0", + "=> (x0 goal not_e@type and_i p4).", + "c x1", + "=> (x1 p3@type and_el@type p3 and_el).", + "c x1", + "=> (x1 p13@type p13@type p13 p13).", + "c x0", + "=> (x0 and_er@type p@type and_er p)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2327, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p0@type p0).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : 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-> (not 'P) -> 'P -> false])))]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c x0", + "=> (x0 p3@type not_i@type p3 not_i).", + "c and_el", + "=> (and_el p3@type not_i@type p6).", + "c and_er", + "=> (and_er p3@type not_i@type p6).", + "intro.", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 508, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c em", + "=> (em em@type).", + "a x0", + "=> (iff (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a iff_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a x", + "=> (iff (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q 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"a x0", + "=> false.", + "a not_e", + "=> (not [false -> [false -> ('P : prop) -> 'P]]); [false -> [false -> ('P : prop) -> 'P]].", + "a x0", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2595, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c x1", + "=> (x1 not_i@type iff_el@type not_i).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false]); [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false].", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type not_e@type p).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0); x0.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not x0)].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal22).", + "a x2", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c x1", + "=> (x1 em@type p3@type em).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1545, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal em@type or_il).", + "c x", + "=> (x iff_i@type p@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type p@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2243, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal14 x).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (or x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : 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-> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 403, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q 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(iff 'P 'Q) -> ['Q -> 'P]]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal13).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L0_5" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 37121, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 252, + "actions": [ + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0).", + "c em", + "=> (em x0).", + "a or_e", + "=> [x0 -> (not x0)]; [(not x0) -> (not x0)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> 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"=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal not_e@type or_ir).", + "c x", + "=> (x iff_i@type or_il@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> (not 'P) -> 'P -> false]))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7373, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_ir@type exfalso).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 7359, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type p@type p0 p).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]].", + "c 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(iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)]; [(not [false -> ('P : prop) -> 'P]) -> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)].", + "a x", + "=> (iff [false -> ('P : prop) -> 'P] (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6856, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [false -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + 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['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", 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(not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6471, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] false); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [false -> ('P : prop) -> 'P] false)]; [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> (or [false -> ('P : prop) -> 'P] false)].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> ('R : 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-> ['P -> false] -> (not 'P)] -> false]))].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [false -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a x1", + "=> (or (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) [[false -> ('P : prop) -> 'P] -> false]); [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]]; [[[false -> ('P : prop) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3440, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x3", + "=> (x3 not_e@type em@type em).", + "c x3", + "=> (x3 or_ir@type p2@type p2).", + "a exfalso", + "=> false.", + "a x1", + "=> (not x0); x0.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x3", + "=> (x3 p0@type@2 not_e@type x).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> 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'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a or_e", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('A : prop) -> (not 'A) -> 'A -> false]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1457, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x goal or_e@type not_e).", + "c x", + "=> (x iff_i@type not_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6323, + "actions": [ + 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'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x0", + "=> (x0 or_e@type goal5 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type p0@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] x); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9564, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not x) -> x -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "c x0", + "=> (x0 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-> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 547, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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+ "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p4@type@2).", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "a x1", + "=> (or (or (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) (not (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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(not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_il@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> .", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em goal6).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em or_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 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-> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> false].", + "a x0", + "=> (and [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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"c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2189, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal15 iff_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso iff_i).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 543, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x1", + "=> (not [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]); [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1482, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a not_e", + "=> (not (not x)); (not x).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] 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'Q)]).", + "a or_e", + "=> [[('A : prop) -> ['A -> false] -> (not 'A)] -> (and [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('A : prop) -> ['A -> false] -> (not 'A)]) -> (and [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1477, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + 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prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ['A -> false] -> (not 'A)]); [('A : prop) -> ['A -> false] -> (not 'A)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ['A -> false] -> (not 'A)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ['A -> false] -> (not 'A)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2059, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type goal15 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 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"=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or (not (not false)) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(not (not false)) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not (not false)) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (not (not false)) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> 'A -> (not (not 'A))]); [('A : prop) -> 'A -> (not (not 'A))].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> 'A -> (not (not 'A))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('A : prop) -> 'A -> (not (not 'A))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> 'A -> (not (not 'A))])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> 'A -> (not (not 'A))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> (not (not x))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2276, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p0@type p0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p1@type or_e@type or_e).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 642, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]].", + "a x", + "=> (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]).", + "a x", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) false).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) false)]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) false)).", + "a x", + "=> (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) false))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) false)))]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) false)))].", + "intro.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> false]].", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or false (not false)))); (not (or false (not false))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(or false (not false)) -> (not (not (or false (not false))))]; [(not (or false (not false))) -> (not (not (or false (not false))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (not (or false (not false)))) -> false]; [(not (not (not (or false (not false))))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + 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'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x", + "=> (x iff_el@type).", + "c x", + "=> (x not_e@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em goal2).", + "c em", + "=> (em and_el@type).", + "intro.", + "c x", + "=> (x goal).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "c x", + "=> (x or_il@type).", + "c x", + "=> (x p1@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))." + ] + } + ], + "problem": "extrinsic_L1_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 19578, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a 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'B]]]])))]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p2@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2762, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 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+ "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "c x1", + "=> (x1 iff_i@type not_e@type x).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 goal9 not_e@type x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]].", + "c x2", + "=> (x2 em@type and_i@type em and_i).", + "c x2", + "=> (x2 iff_i@type iff_el@type iff_i iff_el).", + "c x2", + "=> (x2 p2@type or_ir@type p2 x1).", + "c x1", + "=> (x1 goal19 not_e@type x).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 444, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false].", + "intro.", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false] -> false]; [(not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]) -> false].", + "a x", + "=> (and [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false] -> false] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false] -> false] false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false] -> false] false)]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [false -> ('P : prop) -> 'P]))]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [false -> ('P : prop) -> 'P]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [false -> ('P : prop) -> 'P]))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [false -> ('P : prop) -> 'P]))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1983, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))].", + "a x1", + 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('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]]] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]])) false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]]] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) 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prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]])) false)))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]]] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]])) false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 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-> 'P]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em not_e@type).", + "c not_e", + "=> (not_e and_er@type x and_er).", + "a exfalso", + "=> .", + "c not_e", + "=> (not_e and_er@type x and_er).", + "c em", + "=> (em p3@type).", + "c em", + "=> (em p2@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])) -> false].", + "a x", + "=> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]) -> false] [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]).", + "a and_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]) -> false]; [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]))]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) -> (or [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> [false -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [false -> [false -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 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'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2347, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c x0", + "=> (x0 p2@type and_el@type and_el).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])); (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 27, + "evals_used": 259, + "actions": [ + "a exfalso", + "=> false.", + "c 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(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]); [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 564, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x", + "=> (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (and false (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])).", + "c 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[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x2", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal3).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x3", + "=> (x3 x1).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7513, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> false].", + "a x", + "=> (or [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) [false -> ('P : prop) -> 'P]); [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]]; [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]] [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]] -> (or (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) [false -> ('P : prop) -> 'P])]; [[[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false] -> (or (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not false)]; [(not false) -> (not false)].", + "a or_e", + "=> [false -> [false -> (not false)]]; [(not false) -> [false -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not false) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "c x0", + "=> (x0 not_i@type or_il@type not_i or_il).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_il@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "intro.", + "c x0", + "=> (x0 p3@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 533, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]); [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])]].", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])]]].", + "c em", + "=> (em p0@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> 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'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]])) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)])))])).", + "a x0" + ] + }, + { + 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-> false]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [x -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not x) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> (and 'A 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "c not_e", + "=> (not_e p0@type x2 p0).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e p0@type x2 x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "intro.", + "c x2", + "=> (x2 exfalso@type p@type exfalso p).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", 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-> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not (not false)); (not false).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not false))].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_el@type p4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or false 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prop) -> (or 'A 'B) -> (or 'B 'A)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]].", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]].", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]]]; [false -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]]].", + "a x2", + "=> (or [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]])); [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)].", + "a x2", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [[('P : prop) -> (or 'P (not 'P))] -> (or [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]]))]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]]))].", + "c x1", + "=> (x1 p1@type p1@type p1).", + "a x1", + "=> ." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 382, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]; [(not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", 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+ "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6322, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + 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x0); x0.", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c x3", + "=> (x3 p0@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + 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'P)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1395, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + 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-> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q 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false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] 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(iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e iff_er@type x1 iff_er).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1463, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [false -> [false -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]))].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not (not [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]))]]; [(not [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]) -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not (not [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]))]].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> (iff 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"actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> 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+ "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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-> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]); [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> 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-> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]].", + "c x1", + "=> (x1 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 689, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", 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-> ['P -> 'Q]])) -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 goal16 p1@type p1).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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"c em", + "=> (em iff_el@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [(or x x) -> x]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not 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-> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a x0", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a iff_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [false -> [('P : prop) -> (not 'P) -> 'P -> false]].", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]] -> false].", + "a x3", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]] false).", + "a iff_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]] -> false]; [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]]].", + "intro.", + "a exfalso", + "=> false.", + "c x5", + "=> (x5 x0).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 549, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff (or 'A 'A) 'A)]].", + "intro.", + "intro.", + "a iff_i", + "=> [(or x0 x0) -> x0]; [x0 -> (or x0 x0)].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or x0 x0) -> x0]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or x0 x0) -> x0]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> (iff (or 'A 'A) 'A)]); [('A : prop) -> (iff (or 'A 'A) 'A)].", + "a not_i", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not (not [('A : prop) -> (iff (or 'A 'A) 'A)]))); (not (not [('A : prop) -> (iff (or 'A 'A) 'A)])).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[[('A : prop) -> (iff (or 'A 'A) 'A)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 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false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (or 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a x2", + "=> (not [[[('A : prop) -> (iff (or 'A 'A) 'A)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]); [[[('A : prop) -> (iff (or 'A 'A) 'A)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em p1@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a and_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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+ "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P 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(iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 310, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "a exfalso", + 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(and x false) -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(and x false) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "c em", + "=> (em goal0@1).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4042, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not false)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x", + "=> (x or_ir@type goal3 or_ir).", + "c x", + "=> (x or_il@type p@type@2 or_il).", + "a exfalso", + "=> false.", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "c x", + "=> (x p3@type p3@type@2 p3).", + "c x", + "=> (x p0@type p5@type p0).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 374, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) -> false]; [(not (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)]))) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [(or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) -> false]; [(not (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)]))) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7513, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff (and 'A false) false)]); [('A : prop) -> (iff (and 'A false) false)].", + "a not_i", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [false -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('A : prop) -> (iff (and 'A false) false)] -> false] -> false]; [(not [[('A : prop) -> (iff (and 'A false) false)] -> false]) -> false].", + "a x", + "=> (or (not [[('A : prop) -> (iff (and 'A false) false)] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(not [[('A : prop) -> (iff (and 'A false) false)] -> false]) -> [[[('A : prop) -> (iff (and 'A false) false)] -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('A : prop) -> (iff (and 'A false) false)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('A : prop) -> (iff (and 'A false) false)] -> false]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not [[('A : prop) -> (iff (and 'A false) false)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('A : prop) -> (iff (and 'A false) false)] -> false])].", + "a x", + "=> (or [('A : prop) -> (iff (and 'A false) false)] false); [[('A : prop) -> (iff (and 'A false) false)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [false -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 310, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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-> ['P -> false] -> (not 'P)])))))))) (not [('P : prop) -> ['P -> false] -> (not 'P)])); [(or (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))) (not (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))))) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P 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-> (not 'P)])))))) -> (or (or (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))) (not (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))))) (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 441, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a or_e", + "=> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]; [(not (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5938, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + 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-> false]]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + 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'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('A : prop) -> (iff 'A 'A)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]])]; [(not 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or 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prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false])]].", + "a x0", + "=> (and (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + 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(iff 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6730, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]); [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]]; [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]] -> (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 623, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a 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-> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not x); x.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2420, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false])]].", + "a x0", + "=> (and (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 456, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; 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(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (not (not [('P : prop) -> ('Q : 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'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]].", + "c x2", + "=> (x2 p0@type goal14 p0).", + "c x2", + "=> (x2 iff_er@type goal13 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false]]; [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [('P : prop) -> ['P -> false] -> (not 'P)]); [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type goal2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]))).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0" + ] + } + ], + "problem": "extrinsic_L2_13" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 21567, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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('Q : prop) -> 'P -> (or 'P 'Q)] false)]; [(iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) -> [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)]; [(iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) -> [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]].", + "intro.", + "c em", + "=> (em false).", + "c em", + "=> (em p1@type).", + "a x0", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [false -> [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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-> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]); [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a not_i", + "=> [[false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false])]].", + "a x0", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 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-> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); 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-> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) 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-> 'C] -> ['A -> ['B -> 'C]]])))].", + "a x2", + "=> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])).", + "a x2", + "=> (and (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal11).", + "a x2", + "=> (and (and (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])]]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])]].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))] -> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])]]]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))]) -> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "a exfalso", + "=> false.", + "a x2", + "=> (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x2", + "=> (and (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 404, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> 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false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]))) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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"=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false])); (not [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))]); [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]])); [[[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])] [false -> ('P : prop) -> 'P]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> false] [('P : prop) -> (or 'P (not 'P))])] -> (or [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]))]; [[false -> ('P : prop) -> 'P] -> (or [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2466, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x1", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type 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-> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6472, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [false -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> (or 'P (not 'P))] [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em 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false] -> (not (not x0))]]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not x0))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a x3", + "=> .", + "c em", + "=> (em goal11).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 383, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; 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+ "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2040, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]] -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [false -> [false -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type 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'Q]]) -> false].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", 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false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", 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false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 goal11).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "intro.", + "c x1", + "=> (x1 or_e).", + "intro.", + "a not_e", + "=> (not (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))); (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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[('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x3", + "=> .", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em goal7).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]." + ] + }, + { + "mode": 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+ "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1859, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type and_el@type and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]].", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])].", + "intro.", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]] -> false].", + "intro.", + "c x3", + "=> (x3 not_e).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "c x3", + "=> (x3 x).", + "c x3", + "=> (x3 x1).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]])].", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x3", + "=> (x3 x2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 413, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + 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'Q)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + 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'P)])].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]; [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7031, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]); [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", 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: prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [false -> ('P : prop) -> 'P]); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [false -> ('P : prop) -> 'P])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [false -> [false -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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-> ['P -> 'Q]]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type@2 iff_el@type iff_el).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 467, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em goal15).", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 285, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e" + ] + } + ], + "problem": "extrinsic_L3_8" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 28754, + 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-> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]))]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2418, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type and_i@type and_i).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal11 iff_er@type iff_er).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 657, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a x", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a x", + "=> (and (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (and (and (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) 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[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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+ "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 371, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P 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prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false).", + "a or_il", + "=> .", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]) -> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2000, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> 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+ "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x1", + "=> (x1 p4@type or_ir@type x1).", + "c em", + "=> (em p5@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 or_ir).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 416, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false]; (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (and [[false -> ('P : prop) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))])]; [(not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and [[false -> ('P : prop) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [false -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]] -> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em p@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 527, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : 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'P]))) -> false].", + "c em", + "=> (em p6@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x1", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> false.", + "a 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false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2137, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]].", + "a exfalso", + "=> false.", + 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_er@type p2 and_er).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1326, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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(not 'P))] -> false]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 476, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> 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[(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]]]; [(not (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "intro.", + "a or_e", + "=> 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-> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[(not x) -> [x -> false]] -> false]].", + "c iff_el", + "=> (iff_el p5@type@1 p5@type@2 p5)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 667, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff 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-> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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: prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P 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-> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [x -> false]); [x -> false].", + "a or_e", + "=> [false -> (not [x -> false])]; [(not false) -> (not [x -> false])].", + "a x1", + "=> (iff (not [x -> false]) false).", + "a or_e", + "=> [false -> (iff (not [x -> false]) false)]; [(not false) -> (iff (not [x -> false]) false)].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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"a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ['P -> false] 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('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + 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('P : prop) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2137, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + 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'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 624, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(or x (and x x2)) -> x]; [x -> (or x (and x x2))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or x (and x x2)) -> x]); [(or x (and x x2)) -> x].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + 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(or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type@2).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]) -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 455, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c not_e", + "=> (not_e and_er@type x and_er).", + "c em", 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('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a x0", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]].", + "intro.", + "c em", + "=> (em or_e@type).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 503, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) 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-> (not 'P) -> 'P -> false])].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]] -> false]; [(not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]) -> false].", + "c em", + "=> (em goal12)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 562, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 p2@type)." + ] + } + ], + "problem": "extrinsic_L3_15" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 25467, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a 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(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))].", + "intro.", + "c x", + "=> (x p0@type p@type p0 p).", + "c and_er", + "=> (and_er p0@type p@type p5).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [false -> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]; [(not false) -> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))].", + "c em", + "=> (em not_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 621, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p5@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or false (not false)) -> false]; [(not (or false (not false))) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "intro.", + "c em", + "=> (em goal7).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em not_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3879, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em exfalso@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c x0", + "=> (x0 iff_i@type and_i@type iff_i).", + "c x0", + "=> (x0 or_e@type not_i@type or_e).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 and_er@type goal and_er).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + 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false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))))); (not (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not (not (or [false -> ('P : prop) 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-> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type).", + "c em", + "=> (em p3@type).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1399, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x0", + "=> (x0 em@type or_il@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> 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exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [[[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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: prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 637, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(and x (or x x2)) -> x]; [x -> (and x (or x x2))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('B : prop) -> (iff (and x (or x 'B)) x)]); [('B : 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[[('P : prop) -> (not 'P) -> 'P -> false] -> (or [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]]." + ] + } + ], + "problem": "extrinsic_L3_16" + }, + { + "solved": false, + "greedy_solved": false, + 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['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not x0) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]) -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x2", + "=> false.", + "a x", + "=> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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false] -> (not 'P)]) -> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1405, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P 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prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 626, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2373, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not x)].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type p3@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)] -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))))]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))))].", + "intro." + ] + }, + { + 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false].", + "c em", + "=> (em goal1).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em p@type).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e" + ] + } + ], + "problem": "extrinsic_L3_19" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 15, + "evals_used": 22798, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 163, + "actions": [ + "c em", 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-> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]))] -> false]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro.", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 12270, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "c x", + "=> (x or_ir@type and_i@type or_ir x).", + "c and_el", + "=> (and_el or_ir@type and_i@type p).", + "c p0", + "=> (p0 not_i@type iff_er@type iff_er).", + "c p0", + "=> (p0 exfalso@type not_i@type not_i).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c p0", + "=> (p0 p2@type p1@type p1).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x", + "=> (x iff_er@type not_e@type iff_er not_e).", + "c p0", + "=> (p0 and_el@type iff_el@type iff_el).", + "c em", + "=> (em p4@type).", + "c p0", + "=> (p0 false not_i@type not_i).", + "c x", + "=> (x and_er@type 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(or false (not false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1652, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_el@type p4@type@2 iff_el).", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 or_e@type or_e@type or_e or_e).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el or_e@type or_e@type p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 938, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not x); x.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not x)]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not x)].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not x)].", + "a x0", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a x0", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a x1", + "=> (iff (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false).", + "a iff_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [false -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x0", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 578, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not x0); x0.", + "a not_i", + "=> [x0 -> false].", + "intro.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 p3@type@2).", + "c x3", + "=> (x3 goal7).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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"=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal5 exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])); (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]))]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> (not (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7241, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (not (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]); [(not (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (not [false -> ('P : prop) -> 'P])).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [false -> ('P : prop) -> 'P]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> (not (not [false -> ('P : prop) -> 'P]))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el 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false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x1", + "=> (x1 iff_i@type not_e@type x).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 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false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 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(iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2278, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 not_i@type and_i@type and_i).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p1@type or_e@type or_e).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 468, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]]].", + "c em", + "=> (em exfalso@type).", + 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(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]])])))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]])])))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P 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or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]].", + "intro.", + "a x", + "=> (or (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])))] 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[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1408, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not 'A)) -> false]); [('A : prop) -> (iff 'A (not 'A)) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + 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['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (or 'P (not 'P))] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 501, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(iff x (not x)) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(iff x (not x)) -> false]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "c em", + "=> (em not_i@type).", + "c iff_er", + "=> (iff_er x x2@type@2 x2).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not false)); (not false).", + "a or_e", + "=> [false -> (not (not false))]; [(not false) -> (not (not false))].", + "c iff_el", + "=> (iff_el x x2@type@2 x2).", + "c em", + "=> (em x).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not false))].", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]]]].", + "intro.", + "a x4", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]]).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]] -> [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]].", + "c x4", + "=> (x4 x x2@type@2 x2).", + "a exfalso", + "=> .", + "c x4", + "=> (x4 x x2@type@2 x2).", + "a x4", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": 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prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))) -> false]].", + "c x1", + "=> (x1 em@type p8@type p8).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 459, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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: prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 623, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not 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['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, 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or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "c em", + "=> (em x).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('C : prop) -> [x -> [x0 -> 'C]] -> [(not (not x)) -> [(not (not x0)) -> (not (not 'C))]]]]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('C : prop) -> [x -> [x0 -> 'C]] -> [(not (not x)) -> [(not (not x0)) -> (not (not 'C))]]]]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "a x4", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c x2", + "=> (x2 x4).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('C : prop) -> [x -> [x0 -> 'C]] -> [(not (not x)) -> [(not (not x0)) -> (not (not 'C))]]]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('C : prop) -> [x -> [x0 -> 'C]] -> [(not (not x)) -> [(not (not x0)) -> (not (not 'C))]]]]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('C : prop) -> [x -> [x0 -> 'C]] -> [(not (not x)) -> [(not (not x0)) -> (not (not 'C))]]]]]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('C : prop) -> [x -> [x0 -> 'C]] -> [(not (not x)) -> [(not (not x0)) -> (not (not 'C))]]]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('C : prop) -> [x -> [x0 -> 'C]] -> [(not (not x)) -> [(not (not x0)) -> (not (not 'C))]]]]])) -> [[[('P 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false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])].", + "c em", + "=> (em em@type).", + "a x0", + "=> (iff (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a iff_i", + "=> [(not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]) -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])]; [(not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]) -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]].", + "c em", + "=> (em 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false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6665, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])); [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]))]; [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not false) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not false) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a or_e", + "=> [false -> [(not false) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]; [(not false) -> [(not 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p8@type@2).", + "c em", + "=> (em or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 583, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not 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false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 611, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))); (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> 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-> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]; [(not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> 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-> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]); [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e not_i@type x1 not_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]] [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]] -> [false -> [false -> false]]]; [[('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] -> [false -> [false -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10767, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em exfalso@type).", + "a iff_i", + "=> [(not (not (and x x2))) -> (and (not (not x)) (not (not x2)))]; [(and (not (not x)) (not (not x2))) -> (not (not (and x x2)))].", + "c and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 x p3@type p3).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir p9).", + "c x1", + "=> (x1 not_i@type p5@type p6 p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false p@type p).", + "c x1", + "=> (x1 iff_el@type and_i@type iff_el and_i).", + "c and_er", + "=> (and_er iff_el@type and_i@type p14).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x0", + "=> (x0 p10@type iff_i@type p10 iff_i).", + "c em", + "=> (em p8@type).", + "c em", + "=> (em p17@type@2).", + "c x1", + "=> (x1 p14@type p16@type p14 p16).", + "c p15", + "=> (p15 p11@type p14@type p11 p14).", + "c and_el", + "=> (and_el p1@type p0@type p7)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2786, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) 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or_e", + "=> [(or [('A : prop) -> [(not (not 'A)) -> 'A]] (not [('A : prop) -> [(not (not 'A)) -> 'A]])) -> [(or [('A : prop) -> [(not (not 'A)) -> 'A]] (not [('A : prop) -> [(not (not 'A)) -> 'A]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not (or [('A : prop) -> [(not (not 'A)) -> 'A]] (not [('A : prop) -> [(not (not 'A)) -> 'A]]))) -> [(or [('A : prop) -> [(not (not 'A)) -> 'A]] (not [('A : prop) -> [(not (not 'A)) -> 'A]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em goal10).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not (not 'A)) -> 'A]]]); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 468, + "actions": 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false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 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-> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P 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-> ['P -> false] -> (not 'P)] -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])); [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]))]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + 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(iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e 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-> ['B -> 'A]]] -> (and (not (and [('P : prop) -> (or 'P (not 'P))] false)) (and (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]])) false))]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]] -> (and (not (and [('P : prop) -> (or 'P (not 'P))] false)) (and (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]])) false))]].", + "intro.", + "a x", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]] -> (and (not (and [('P : prop) -> (or 'P (not 'P))] false)) (and (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 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+ "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c em", + "=> (em p@type@2).", + "c x0", + "=> (x0 iff_i).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 iff_i).", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 443, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c not_e", + "=> (not_e iff_er@type x0 iff_er).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em goal9).", + "c em", + "=> (em goal).", + "c em", + "=> (em p4@type).", + "c not_e", + "=> (not_e iff_er@type x0 iff_er).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]) -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]]]].", + "intro.", + "c x1", + "=> (x1 iff_er@type x0 iff_er).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1989, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "c x1", + "=> (x1 exfalso@type p0@type exfalso p0).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]); [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]].", + "c and_el", + "=> (and_el exfalso@type p0@type p3).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [false -> ('P : prop) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x1", + "=> (x1 exfalso@type em@type exfalso em).", + "c and_el", + "=> (and_el exfalso@type em@type p5).", + "intro.", + "a p4", + "=> false.", + "a p4", + "=> false.", + "c and_er", + "=> (and_er exfalso@type p0@type p3).", + "c x1", + "=> (x1 exfalso@type and_i@type p4 x1).", + "a x3", + "=> false.", + "c and_er", + "=> (and_er exfalso@type and_i@type p8).", + "a x2", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x3", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5246, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]); [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "c x1", + "=> (x1 iff_i@type p@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])); (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 goal9 p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]].", + "c x2", + "=> (x2 goal and_i@type x1 and_i).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p2@type or_e@type p2 or_e).", + "c x1", + "=> (x1 goal19 goal0).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))]; [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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(iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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(and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c x", + "=> (x goal).", + "c x", + "=> (x p1@type).", + "a exfalso", + "=> false.", + "c x", + "=> (x p3@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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'R] -> 'R]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p4@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em p5@type@2).", + "c em" + ] + }, + { + "mode": "sample", 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(not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + 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'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]].", + "c p8", + "=> (p8 goal p1@type p1).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 708, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 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: prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))))).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]].", + "a x2", + "=> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]]).", + "a x2", + "=> (and (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))) (and [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]])).", + "a x2", + "=> (and (and [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]]) (and (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))) (and [false -> ('P : prop) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> (or 'P (not 'P))]) (and false false))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]]))).", + "c em", + "=> (em goal19).", + "c em", + "=> (em x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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+ "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1859, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c x0", + "=> (x0 iff_i@type p@type p).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type p2@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1265, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 516, + "actions": [ + "intro.", + "intro.", + "intro.", + "c em", + "=> (em x0).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [x0 -> 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x1", + "=> (x1 p4@type goal6 p4).", + "c em", + "=> (em p5@type).", + "c x3", + "=> (x3 p1@type exfalso@type p1 exfalso).", + "c x3", + "=> (x3 p@type or_il@type x2 or_il).", + "c and_er" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2976, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em 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-> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [x -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not x) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [x -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [x -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [x -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [x -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]].", + "intro.", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2063, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", 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false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 51, + "evals_used": 5387, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) 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[(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c p8", + "=> (p8 p@type@2 and_i@type and_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6188, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x2", + "=> (x2 or_il@type not_i@type not_i).", + "c x2", + "=> (x2 p1@type@2 and_i@type and_i).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x2", + "=> (x2 p0@type iff_er@type iff_er).", + "c em", + "=> (em p3@type).", + "c x2", + "=> (x2 or_ir@type p4@type p4).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]]; [(or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]].", + "c x2", + "=> (x2 goal10 exfalso@type exfalso).", + "c x2", + "=> (x2 p1@type or_ir@type or_ir).", + "c x2", + "=> (x2 goal12 and_i@type and_i).", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]).", + "c em", + "=> (em x0)." + ] + }, + { + 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'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> false]; [(not (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])) -> false].", + "a x", + "=> (and [(not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a and_i", + "=> [(not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> 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(or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7312, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 54, + "evals_used": 5837, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p3@type not_e p3).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (and [('P : prop) -> (not 'P) -> 'P -> false] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]))))).", + "c x0", + "=> (x0 em@type or_e@type em or_e)." + ] + } + ], + "problem": 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: prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 796, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]); [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]].", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 463, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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false])]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]].", + "intro.", + "c em", + "=> (em goal21).", + "a x2", + "=> false.", + "a x", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "c x", + "=> (x not_i@type iff_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : 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'Q]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> 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false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2179, + "actions": [ + "c em", + "=> (em or_il@type).", + "a 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['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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: prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or x [x -> 'B])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q 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(not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]].", + "a p3", + "=> (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]).", + "a p3", + "=> (not [(not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]) -> (not (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]))]).", + "a p3", + "=> (not [(not [(not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]) -> (not (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]))]) -> (not (not [(not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]) -> (not (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]))]))]).", + "a p2", + "=> (not [(not [(not [(not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]) -> (not (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]))]) -> (not (not [(not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]) -> (not (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]))]))]) -> (not (not [(not [(not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]) -> (not (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]))]) -> (not (not [(not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]) -> (not (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])]))]))]))]).", + "c em", + "=> (em goal3)." + ] + }, + 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-> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])) -> false]; [(not (or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]); [('A : prop) -> (not ['A -> (not 'A)]) -> 'A].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c x", + "=> (x not_i@type p4@type x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c em", + "=> (em goal3).", + "intro.", + "c em", + "=> (em goal7).", + "c x", + "=> (x iff_er@type p4@type iff_er).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p6@type).", + "c em", + "=> (em goal12).", + "c em", + "=> (em goal11).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> false]; [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_il", + "=> (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]).", + "c em", + "=> (em or_ir@type).", + "a not_i", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> false].", + "a x1", + "=> (or false [('P : prop) -> ['P -> false] -> (not 'P)]); [false -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> false]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 493, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(not x0) -> x0] -> x0]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "intro.", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal17).", + "c x", + "=> (x or_il@type x3 or_il).", + "c em", + "=> (em p5@type).", + "c x1", + "=> (x1 or_il@type x3 or_il).", + "c x2", + "=> (x2 or_il@type x3 or_il).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> false]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> false].", + "a x", + "=> (and [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> false] [('A : prop) -> [(not 'A) -> 'A] -> 'A]).", + "a and_i", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> false]; [('A : prop) -> [(not 'A) -> 'A] -> 'A].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> [(not 'A) -> 'A] -> 'A] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A])) -> false]; [(not (or [('A : prop) -> [(not 'A) -> 'A] -> 'A] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> [(not 'A) -> 'A] -> 'A] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A])) -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [(or [('A : prop) -> [(not 'A) -> 'A] -> 'A] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A])) -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(or [('A : prop) -> [(not 'A) -> 'A] -> 'A] (not [('A : prop) -> [(not 'A) -> 'A] -> 'A])) -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 449, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2138, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + 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-> false].", + "intro.", + "a x2", + "=> (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]).", + "a x2", + "=> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x1", + "=> (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x2", + "=> (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em goal11).", + "a x2", + "=> (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false])); (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]]].", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x2", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x2", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[[('P : prop) -> (or 'P (not 'P))] -> (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (and (and (iff [('P : prop) -> (or 'P (not 'P))] (and (and false [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (not 'P) -> 'P -> false]))]]]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal19).", + "c em", + "=> (em x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1402, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "c x0", + "=> (x0 em@type or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 2127, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L4_13" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 12, + "evals_used": 17621, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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'P 'Q)] false).", + "a x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7321, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))).", + "a 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(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_ir", + "=> (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 457, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", 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em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]) -> false].", + "c x", + "=> (x not_i@type iff_er@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x goal goal16).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 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not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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em", + "=> (em x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 481, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] (not false)).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; (not false).", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "intro.", + "c em", + "=> (em goal17).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "c em", + "=> (em not_i@type).", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2112, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a not_i", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])); [[false -> ('P : prop) -> 'P] -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not false) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [false -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not false) -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4265, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal2).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", 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"intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P 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+ "c x", + "=> (x and_i@type and_er@type p11 and_er).", + "c x", + "=> (x em@type p15@type em p15).", + "c p11", + "=> (p11 and_i@type p6@type p11 p6).", + "c p0", + "=> (p0 and_el@type iff_er@type iff_er).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c p11", + "=> (p11 p3@type and_er@type p3 and_er).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 519, + "actions": [ + "intro.", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (and x (not x0))); (and x (not x0)).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x0)); (not x0).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a x1", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 778, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c em", + "=> (em and_er@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_e@type not_i@type or_e not_i).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el or_e@type not_i@type p4).", + "a or_e", + "=> [(not x) -> false]; [(not (not x)) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x1", + "=> false.", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8246, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em iff_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))); [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x", + "=> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (or false (not false))); [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or false (not false)) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal8).", + "a x", + "=> (or (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a or_il", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 391, + "actions": [ + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]].", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]].", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a 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+ "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5203, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [false -> ('P : prop) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em 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prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6665, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> 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+ "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]])]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]])]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]])]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]])]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1841, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a not_i", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> false].", + "c x", + "=> (x goal11 or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 510, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]; [(not false) -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]].", + "a or_e", + "=> [false -> [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]]; [(not false) -> [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]); [false -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal3).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2274, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + 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-> [(iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (or (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> (not 'P) -> 'P -> false])) (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))))]]]]; [(iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(iff x0 [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (or (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> (not 'P) -> 'P -> false])) (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))))]]]].", + "c p3", + "=> (p3 p5@type goal3).", + "c p3", + "=> (p3 p4@type@2 goal13).", + "c p3", + "=> (p3 goal15 p8@type@1).", + "c p2" + ] + } + ], + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 16, + "evals_used": 27535, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]))].", + "intro.", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]) -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 565, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "a and_i", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)) false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false).", + "c em", + "=> (em goal).", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)).", + "c em", + "=> (em p@type).", + "a x", + "=> (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false))).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))).", + "a x", + "=> 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-> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false))))))).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))])) -> (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))))))]; [(not (or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]))) -> (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))))))].", + "a x", + "=> (and (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)) false) [(or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))])) -> (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and false (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : 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(iff 'A (not 'B)))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 969, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c x1", + "=> (x1 iff_i@type iff_el@type x2 iff_el).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5204, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c x0", + "=> (x0 goal8 not_i@type not_i).", + "c x0", + "=> (x0 p@type@2 and_er@type and_er).", + "c x0", + "=> (x0 p7@type p8@type p8).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type@2 and_i@type and_i).", + "c x0", + "=> (x0 p3@type p4@type p4).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]; [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "c em", + "=> (em p8@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 491, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + 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-> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (iff false [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x0", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a x0", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5487, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c x1", + "=> (x1 iff_i@type or_il@type).", + "c iff_el", + "=> (iff_el p1@type@1 p1@type@2 p1).", + "c em", + "=> (em p1@type@1).", + "c em", + "=> (em goal7).", + "c x1", + "=> (x1 p1@type@2 p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "intro.", + "c iff_el", + "=> (iff_el p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x p@type@2 p0@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1408, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2074, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> false]; [(not (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 530, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "c em", + "=> (em goal14).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 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-> 'P]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [[('P : prop) -> (or 'P (not 'P))] -> false])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + 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['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [false -> [false -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [false -> [false -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 10649, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and (not x) (not 'B))) (iff x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or (and x 'B) (and (not x) (not 'B))) (iff x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and (not x) (not 'B))) (iff x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or (and x 'B) (and (not x) (not 'B))) (iff x 'B))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em not_i@type).", + "a iff_i", + "=> [(or (and x x2) (and (not x) (not x2))) -> (iff x x2)]; [(iff x x2) -> (or (and x x2) (and (not x) (not x2)))].", + "c and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 p0@type p3@type p3).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir p9).", + "c x1", + "=> (x1 not_i@type p5@type p6 p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false em@type em).", + "c x1", + "=> (x1 p11@type 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('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false))))))).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and [('P : prop) -> (not 'P) -> 'P -> false] (and (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false)))))))]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> (and [('P : prop) -> (not 'P) -> 'P -> false] (and (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 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prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false)))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "c em", + "=> (em goal9).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); false.", + "a or_e", + "=> [(and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false) false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false) false)) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false) false) -> false]; [(not (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false) false)) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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'P)]))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal12).", + "intro.", + "a x2", + "=> (iff (not (not [('P : prop) -> ['P -> false] -> (not 'P)])) [false -> ('P : prop) -> 'P]).", + "a iff_i", + "=> [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [false -> ('P : prop) -> 'P]]; [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [false -> ('P : prop) -> 'P]]); [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [false -> ('P : prop) -> 'P]].", + "a x1", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]])); (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]).", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]) -> false].", + "a x2", + "=> (iff false (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]])).", + "a x0", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]) -> false].", + "a x2", + "=> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]) false)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 884, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])); (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]).", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]) -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x3", + "=> (x3 iff_i@type exfalso@type x0 exfalso).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 503, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 428, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> 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(not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a or_e", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]; [(not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "c x1", + "=> (x1 or_e@type iff_i@type or_e iff_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type iff_i@type p1).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a p4", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_i@type).", + "a p4", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> (or 'P (not 'P))] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c em", + "=> (em p6@type).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a p4", + "=> (or (not (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))))) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3269, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x not_i@type iff_er@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x p@type p4@type@2).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 419, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [x -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not x) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2033, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 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'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))); (not (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 451, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not false) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "intro.", + "a or_e", + 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prop) -> (or ['A -> 'B] ['B -> 'C])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em 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['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + 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prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + 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['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] false); [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]]; [false -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 8670, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]].", + "c x0", + "=> (x0 not_i@type 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(iff (or 'A 'B) (or 'A 'C)))] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : 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(or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))])) -> false].", + "a x", + "=> (or [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] -> false] [false -> ('P : prop) -> 'P]); [[[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] -> false] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))])))]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))])))].", + "a x0", + "=> (or [('P : prop) -> 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'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x1", + "=> (x1 p4@type goal6 p4).", + "c em", + "=> (em p5@type).", + "a x3", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))] (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (not (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))))); [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]]]; [(or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (not (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]]].", + "a x3", + "=> (or (not (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))] (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (not (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) x0))]])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 44, + "evals_used": 232, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> 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false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('C : prop) -> [[(or x x0) -> (or x 'C)] -> (or x [x0 -> 'C])]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('C : prop) -> [[(or x x0) -> (or x 'C)] -> (or x [x0 -> 'C])]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a x1", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))]].", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))]]).", + "c em", + "=> (em goal18).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('C : prop) -> [[(or x x0) -> (or x 'C)] -> (or x [x0 -> 'C])]]] (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))]])).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('C : prop) -> [[(or x x0) -> (or x 'C)] -> (or x [x0 -> 'C])]]] (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))]]))).", + "a and_i", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('C : prop) -> [[(or x x0) -> (or x 'C)] -> (or x [x0 -> 'C])]]] (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> (or 'P (not 'P))]))]])).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em goal9).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> false].", + "a x0", + "=> (iff false [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 54, + "evals_used": 6169, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em iff_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a x", + "=> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[false -> ('P : prop) -> 'P] -> (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [false -> ('P : prop) -> 'P])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]) [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_ir", + "=> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c em" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..c098c250dba09b2257c4fc245015969acb452a9e --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,911 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_1 (traces=17 evals=19371) +[ ] - extrinsic_L0_3 (traces=17 evals=26615) +[ ] - extrinsic_L0_2 (traces=14 evals=33770) +[ ] - extrinsic_L0_4 (traces=17 evals=31800) +[ ] - extrinsic_L0_5 (traces=16 evals=33062) +[ ] - extrinsic_L0_6 (traces=13 evals=37121) +[OK ] - extrinsic_L0_10 (traces=5 evals=2024) +[ ] - extrinsic_L0_12 (traces=17 evals=13464) + +thread '' (744945) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false] (x0 [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> (not 'A) -> 'A -> false] not_e not_e)): parameter type (and [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (not 'P) -> 'P -> false]) and value type (and [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> (not 'A) -> 'A -> false]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_7 (traces=17 evals=23036) +[ ] - extrinsic_L0_8 (traces=11 evals=22842) +[ ] - extrinsic_L0_11 (traces=17 evals=17518) + +thread '' (744948) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ['P -> false] -> (not 'P)] (x0 [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] not_i iff_er)): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ['P -> false] -> (not 'P)]) and value type (and [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_9 (traces=14 evals=37186) +[ ] - extrinsic_L0_13 (traces=17 evals=28863) +[ ] - extrinsic_L0_14 (traces=16 evals=21387) + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_1 (traces=17 evals=26241) + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_2 (traces=13 evals=19578) +[ ] - extrinsic_L1_3 (traces=16 evals=30446) +[ ] - extrinsic_L1_4 (traces=15 evals=36283) +[ ] - extrinsic_L2_1 (traces=17 evals=25807) + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_2 (traces=15 evals=28949) +[ ] - extrinsic_L2_3 (traces=15 evals=12411) +[ ] - extrinsic_L2_5 (traces=8 evals=13577) +[ ] - extrinsic_L2_4 (traces=14 evals=22850) +[ ] - extrinsic_L2_6 (traces=17 evals=27322) +[ ] - extrinsic_L2_7 (traces=11 evals=19428) + +thread '' (744941) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_8 (traces=17 evals=14432) +[ ] - extrinsic_L2_12 (traces=17 evals=27496) +[ ] - extrinsic_L2_9 (traces=14 evals=27677) +[ ] - extrinsic_L2_10 (traces=12 evals=17609) +[ ] - extrinsic_L2_11 (traces=14 evals=27166) +[ ] - extrinsic_L2_13 (traces=13 evals=37705) +[ ] - extrinsic_L3_1 (traces=17 evals=21567) + +thread '' (744941) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744941) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_4 (traces=17 evals=19338) +[ ] - extrinsic_L3_2 (traces=13 evals=16972) + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_3 (traces=17 evals=28723) + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_5 (traces=17 evals=22927) + +thread '' (744947) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (744947) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_6 (traces=15 evals=20740) +[ ] - extrinsic_L3_7 (traces=17 evals=23948) +[ ] - extrinsic_L3_11 (traces=17 evals=16322) + +thread '' (744941) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_8 (traces=16 evals=36898) + +thread '' (744941) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_9 (traces=17 evals=28754) +[ ] - extrinsic_L3_10 (traces=15 evals=25093) +[ ] - extrinsic_L3_12 (traces=17 evals=20758) +[ ] - extrinsic_L3_15 (traces=17 evals=12739) +[ ] - extrinsic_L3_13 (traces=15 evals=14187) + +thread '' (744947) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744947) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744947) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744947) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_18 (traces=17 evals=16720) +[ ] - extrinsic_L3_14 (traces=15 evals=14742) + +thread '' (744947) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_17 (traces=17 evals=28173) +[ ] - extrinsic_L3_16 (traces=17 evals=25467) +[ ] - extrinsic_L3_23 (traces=17 evals=13472) +[ ] - extrinsic_L3_24 (traces=17 evals=17349) + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=12 evals=21923) + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_20 (traces=15 evals=22798) + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_21 (traces=14 evals=25516) +[ ] - extrinsic_L3_22 (traces=17 evals=31454) + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_27 (traces=17 evals=24739) +[ ] - extrinsic_L3_26 (traces=17 evals=17652) +[ ] - extrinsic_L3_25 (traces=14 evals=18124) +[ ] - extrinsic_L3_28 (traces=9 evals=8088) +[ ] - extrinsic_L3_29 (traces=15 evals=24263) +[ ] - extrinsic_L4_1 (traces=6 evals=19724) + +thread '' (744941) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744941) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_3 (traces=17 evals=17659) +[ ] - extrinsic_L4_4 (traces=17 evals=18479) + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_2 (traces=17 evals=18057) + +thread '' (744948) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_5 (traces=17 evals=27261) +[ ] - extrinsic_L4_6 (traces=17 evals=24047) +[ ] - extrinsic_L4_7 (traces=13 evals=34513) +[ ] - extrinsic_L4_9 (traces=17 evals=14239) +[ ] - extrinsic_L4_11 (traces=17 evals=15017) +[ ] - extrinsic_L4_8 (traces=13 evals=35187) +[ ] - extrinsic_L4_10 (traces=17 evals=33085) + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_12 (traces=15 evals=23981) +[ ] - extrinsic_L4_13 (traces=11 evals=42488) +[ ] - extrinsic_L4_14 (traces=12 evals=17621) +[ ] - extrinsic_L5_1 (traces=11 evals=30005) +[ ] - extrinsic_L5_2 (traces=17 evals=24087) +[ ] - extrinsic_L5_5 (traces=17 evals=15445) +[ ] - extrinsic_L5_3 (traces=8 evals=24349) +[ ] - extrinsic_L5_4 (traces=17 evals=26989) +[ ] - extrinsic_L5_6 (traces=8 evals=32563) + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_7 (traces=16 evals=27535) +[ ] - extrinsic_L5_8 (traces=8 evals=13413) +[ ] - extrinsic_L5_10 (traces=15 evals=17934) +[ ] - extrinsic_L5_9 (traces=13 evals=26813) + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744946) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_1 (traces=8 evals=12606) +[ ] - extrinsic_L5_11 (traces=17 evals=82408) + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_3 (traces=3 evals=62444) +[ ] - extrinsic_L6_4 (traces=13 evals=24683) +[ ] - extrinsic_L6_5 (traces=8 evals=15752) +[ ] - extrinsic_L6_2 (traces=9 evals=48213) + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (744944) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_6 (traces=1 evals=166) +[ ] - extrinsic_L6_7 (traces=9 evals=16907) +[ ] - extrinsic_L6_9 (traces=6 evals=56244) +[ ] - extrinsic_L6_8 (traces=2 evals=36650) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 1/94 in 9151.4s diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..5a0a71e9b9f4a14df2b71988d009b25be76cc48f --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log @@ -0,0 +1,224 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_3 (traces=17 evals=20088) +[ ] - extrinsic_L0_1 (traces=17 evals=19332) +[OK ] g extrinsic_L0_8 (traces=1 evals=15) +[ ] - extrinsic_L0_4 (traces=17 evals=37189) +[ ] - extrinsic_L0_2 (traces=13 evals=26529) +[ ] - extrinsic_L0_6 (traces=14 evals=28226) +[ ] - extrinsic_L0_5 (traces=11 evals=18331) +[OK ] - extrinsic_L0_10 (traces=5 evals=1986) +[ ] - extrinsic_L0_7 (traces=11 evals=23866) +[ ] - extrinsic_L0_12 (traces=17 evals=25345) +[ ] - extrinsic_L0_9 (traces=15 evals=23599) +[ ] - extrinsic_L0_11 (traces=13 evals=18903) +[ ] - extrinsic_L0_13 (traces=15 evals=35652) +[ ] - extrinsic_L0_14 (traces=14 evals=23331) + +thread '' (924805) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_2 (traces=17 evals=21025) + +thread '' (924977) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_1 (traces=15 evals=25023) + +thread '' (924977) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924923) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_3 (traces=15 evals=32940) +[ ] - extrinsic_L1_4 (traces=17 evals=34415) +[ ] - extrinsic_L2_2 (traces=17 evals=21078) +[ ] - extrinsic_L2_1 (traces=13 evals=15707) +[ ] - extrinsic_L2_3 (traces=13 evals=16000) + +thread '' (925139) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_4 (traces=16 evals=22569) +[ ] - extrinsic_L2_6 (traces=17 evals=16339) +[ ] - extrinsic_L2_5 (traces=17 evals=18101) +[ ] - extrinsic_L2_8 (traces=17 evals=21676) +[ ] - extrinsic_L2_7 (traces=13 evals=23547) +[ ] - extrinsic_L2_9 (traces=17 evals=23260) +[ ] - extrinsic_L2_10 (traces=17 evals=27961) +[ ] - extrinsic_L2_12 (traces=13 evals=20410) +[ ] - extrinsic_L2_11 (traces=11 evals=15059) +[ ] - extrinsic_L2_13 (traces=11 evals=14202) +[ ] - extrinsic_L3_1 (traces=17 evals=22168) +[ ] - extrinsic_L3_2 (traces=13 evals=15983) +[ ] - extrinsic_L3_6 (traces=17 evals=25088) +[ ] - extrinsic_L3_3 (traces=8 evals=3597) +[ ] - extrinsic_L3_7 (traces=7 evals=6787) +[ ] - extrinsic_L3_5 (traces=1 evals=650) +[ ] - extrinsic_L3_8 (traces=17 evals=22963) +[ ] - extrinsic_L3_9 (traces=15 evals=22453) +[ ] - extrinsic_L3_11 (traces=17 evals=20228) +[ ] - extrinsic_L3_10 (traces=15 evals=16939) +[ ] - extrinsic_L3_4 (traces=1 evals=608) + +thread '' (924923) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_12 (traces=17 evals=16097) +[ ] - extrinsic_L3_14 (traces=17 evals=21165) +[ ] - extrinsic_L3_15 (traces=17 evals=17518) +[ ] - extrinsic_L3_13 (traces=12 evals=10386) + +thread '' (924697) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (924697) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924697) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_16 (traces=13 evals=24426) +[ ] - extrinsic_L3_18 (traces=17 evals=14414) +[ ] - extrinsic_L3_17 (traces=15 evals=32250) +[ ] - extrinsic_L3_19 (traces=13 evals=25677) +[ ] - extrinsic_L3_20 (traces=17 evals=27254) + +thread '' (924977) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_21 (traces=8 evals=11992) +[ ] - extrinsic_L3_22 (traces=15 evals=21792) +[ ] - extrinsic_L3_23 (traces=17 evals=17991) +[ ] - extrinsic_L3_24 (traces=17 evals=26276) +[ ] - extrinsic_L3_25 (traces=17 evals=18865) +[ ] - extrinsic_L3_26 (traces=6 evals=15029) +[ ] - extrinsic_L3_27 (traces=16 evals=23952) +[ ] - extrinsic_L3_28 (traces=13 evals=22574) +[ ] - extrinsic_L4_2 (traces=17 evals=11368) +[ ] - extrinsic_L3_29 (traces=14 evals=19317) +[ ] - extrinsic_L4_1 (traces=14 evals=20374) +[ ] - extrinsic_L4_3 (traces=13 evals=18623) +[ ] - extrinsic_L4_4 (traces=15 evals=25696) +[ ] - extrinsic_L4_6 (traces=17 evals=28489) +[ ] - extrinsic_L4_5 (traces=14 evals=41120) +[ ] - extrinsic_L4_7 (traces=17 evals=27563) +[ ] - extrinsic_L4_8 (traces=15 evals=24289) +[ ] - extrinsic_L4_9 (traces=17 evals=22075) +[ ] - extrinsic_L4_10 (traces=17 evals=23210) +[ ] - extrinsic_L4_11 (traces=17 evals=26439) +[ ] - extrinsic_L4_14 (traces=17 evals=31920) +[ ] - extrinsic_L4_12 (traces=15 evals=28551) +[ ] - extrinsic_L4_13 (traces=12 evals=18221) +[ ] - extrinsic_L5_1 (traces=17 evals=19807) +[ ] - extrinsic_L5_2 (traces=15 evals=21308) +[ ] - extrinsic_L5_5 (traces=17 evals=22044) +[ ] - extrinsic_L5_3 (traces=17 evals=27529) +[ ] - extrinsic_L5_4 (traces=7 evals=22692) +[ ] - extrinsic_L5_6 (traces=17 evals=29576) +[ ] - extrinsic_L5_7 (traces=17 evals=28235) +[ ] - extrinsic_L5_8 (traces=17 evals=25794) + +thread '' (924697) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924697) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924697) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=13 evals=19022) +[ ] - extrinsic_L5_11 (traces=13 evals=17581) +[ ] - extrinsic_L5_10 (traces=6 evals=24193) +[ ] - extrinsic_L6_1 (traces=15 evals=25702) diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..4fcb890a03703ddbe29efbb64641d87f8848dce2 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 50 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s45/train.log b/experiments/learnability/train_policy_only/minimo_0pt/s45/train.log new file mode 100644 index 0000000000000000000000000000000000000000..7c77552efff85d08524b9d8f81d098feb502d5d4 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s45/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_053017-j177opnw +[2026-06-28T05:30:13.398121] Seeded RNGs with seed=45 +[2026-06-28T05:30:13.398379] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-28T05:30:17.039409] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json + 1567 training examples loaded. + +============================================================ +[2026-06-28T05:30:17.041558] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 1567 -> 1567 unique examples + Epoch 1/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 50 total steps, 1567 unique examples (batch_size=64) +[2026-06-28T05:30:27.897370] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:30:27.907128] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s45/2026-06-28_05-30-13/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 50} diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/summary.json b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..d4c7ef5fb7bd5686f09cb9730fd6e8505507b0ed --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_0_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 50 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/ablation_config.json b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/ablation_config.json new file mode 100644 index 0000000000000000000000000000000000000000..b29f0311b244620ff675a52640e8acbf7911f2cf --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/ablation_config.json @@ -0,0 +1,8 @@ +{ + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1, + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json" +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..dc18b8859d29ea6db1eb4947676c501edd217b8b --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json @@ -0,0 +1,1057 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/epoch_2.pt", + "problemset": "extrinsic-95", + "max_pops": 4000, + "max_actions": 0, + "timeout": 600.0, + "workers": 6, + "num_problems": 94, + 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"evals_used": 26537, + "max_open": 22538, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31357, + "max_open": 27358, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26002, + "max_open": 22003, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31341, + "max_open": 27342, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31290, + "max_open": 27291, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31092, + "max_open": 27093, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31007, + "max_open": 27008, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26075, + "max_open": 22076, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25972, + "max_open": 21973, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31298, + "max_open": 27299, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31095, + "max_open": 27096, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..7ba5fa2448ca080fd982494c3e5000955063a7be --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=5 evals=25 maxopen=19) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_5 (solved pops=56 evals=368 maxopen=313) +[OK ] extrinsic_L0_6 (solved pops=57 evals=353 maxopen=297) +[OK ] extrinsic_L0_7 (solved pops=55 evals=353 maxopen=299) +[OK ] extrinsic_L0_3 (solved pops=63 evals=389 maxopen=327) +[OK ] extrinsic_L0_10 (solved pops=7 evals=41 maxopen=35) +[OK ] extrinsic_L0_8 (solved pops=57 evals=358 maxopen=302) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=22 evals=156 maxopen=135) +[OK ] extrinsic_L0_9 (solved pops=52 evals=347 maxopen=280) +[OK ] extrinsic_L0_4 (solved pops=210 evals=1122 maxopen=913) +[OK ] extrinsic_L1_4 (solved pops=15 evals=100 maxopen=84) +[OK ] extrinsic_L0_11 (solved pops=211 evals=1143 maxopen=933) +[OK ] extrinsic_L1_1 (solved pops=214 evals=1173 maxopen=942) +[OK ] extrinsic_L1_2 (solved pops=456 evals=2414 maxopen=1959) +[OK ] extrinsic_L1_3 (solved pops=456 evals=2411 maxopen=1956) +[OK ] extrinsic_L2_1 (solved pops=1255 evals=6827 maxopen=5573) +[OK ] extrinsic_L2_6 (solved pops=1600 evals=9221 maxopen=7622) +[OK ] extrinsic_L2_7 (solved pops=1030 evals=5839 maxopen=4810) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25990 maxopen=21991) +[OK ] extrinsic_L0_14 (solved pops=3989 evals=26296 maxopen=22308) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25874 maxopen=21875) +[OK ] extrinsic_L2_11 (solved pops=22 evals=145 maxopen=122) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25739 maxopen=21740) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25869 maxopen=21870) +[OK ] extrinsic_L2_9 (solved pops=1018 evals=5770 maxopen=4753) +[OK ] extrinsic_L2_12 (solved pops=1331 evals=7571 maxopen=6241) +[ ] extrinsic_L2_8 (budget pops=4000 evals=25752 maxopen=21753) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26370 maxopen=22371) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25796 maxopen=21797) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25876 maxopen=21877) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25800 maxopen=21801) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25834 maxopen=21835) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26040 maxopen=22041) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26024 maxopen=22025) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25758 maxopen=21759) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25826 maxopen=21827) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26012 maxopen=22013) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26177 maxopen=22178) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25986 maxopen=21987) +[ ] extrinsic_L3_11 (budget pops=4000 evals=26122 maxopen=22123) +[OK ] extrinsic_L3_13 (solved pops=3475 evals=22064 maxopen=18590) +[OK ] extrinsic_L3_14 (solved pops=3188 evals=19489 maxopen=16302) +[ ] extrinsic_L3_12 (budget pops=4000 evals=26126 maxopen=22127) +[ ] extrinsic_L3_15 (budget pops=4000 evals=25986 maxopen=21987) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26021 maxopen=22022) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25745 maxopen=21746) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25342 maxopen=21343) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26004 maxopen=22005) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26105 maxopen=22106) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26085 maxopen=22086) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25829 maxopen=21830) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26118 maxopen=22119) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26270 maxopen=22271) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26871 maxopen=22872) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25912 maxopen=21913) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26293 maxopen=22294) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25754 maxopen=21755) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26053 maxopen=22054) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26809 maxopen=22810) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26030 maxopen=22031) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26372 maxopen=22373) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25956 maxopen=21957) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26094 maxopen=22095) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25957 maxopen=21958) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26722 maxopen=22723) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26620 maxopen=22621) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26241 maxopen=22242) +[OK ] extrinsic_L4_12 (solved pops=1332 evals=7314 maxopen=5980) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25595 maxopen=21596) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26261 maxopen=22262) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26084 maxopen=22085) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26287 maxopen=22288) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25774 maxopen=21775) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26197 maxopen=22198) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26267 maxopen=22268) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25690 maxopen=21691) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26091 maxopen=22092) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26547 maxopen=22548) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26504 maxopen=22505) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26307 maxopen=22308) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26368 maxopen=22369) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26537 maxopen=22538) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26002 maxopen=22003) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31357 maxopen=27358) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31341 maxopen=27342) +[ ] extrinsic_L6_4 (budget pops=4000 evals=31092 maxopen=27093) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31290 maxopen=27291) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31007 maxopen=27008) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26075 maxopen=22076) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25972 maxopen=21973) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31298 maxopen=27299) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31095 maxopen=27096) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A 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"max_open": 21796, + "solution_actions": null, + "problem": "extrinsic_L4_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26332, + "max_open": 22333, + "solution_actions": null, + "problem": "extrinsic_L4_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25687, + "max_open": 21688, + "solution_actions": null, + "problem": "extrinsic_L4_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26177, + "max_open": 22178, + "solution_actions": null, + "problem": "extrinsic_L4_11" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 1298, + "evals_used": 7444, + "max_open": 6144, + "solution_actions": [ + "intro.", + "intro.", + "c em", + "=> (em x).", + "a or_e", + "=> [x -> x].", + "intro." + ], + "problem": "extrinsic_L4_12" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25810, + "max_open": 21811, + "solution_actions": null, + "problem": "extrinsic_L4_13" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26112, + "max_open": 22113, + "solution_actions": null, + "problem": "extrinsic_L4_14" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26020, + "max_open": 22021, + "solution_actions": null, + "problem": "extrinsic_L5_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26152, + "max_open": 22153, + "solution_actions": null, + "problem": "extrinsic_L5_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26224, + "max_open": 22225, + "solution_actions": null, + "problem": "extrinsic_L5_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25997, + "max_open": 21998, + "solution_actions": null, + "problem": "extrinsic_L5_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26474, + "max_open": 22475, + "solution_actions": null, + "problem": "extrinsic_L5_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26109, + "max_open": 22110, + "solution_actions": null, + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26150, + "max_open": 22151, + "solution_actions": null, + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26312, + "max_open": 22313, + "solution_actions": null, + "problem": "extrinsic_L5_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26444, + "max_open": 22445, + "solution_actions": null, + "problem": "extrinsic_L5_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26553, + "max_open": 22554, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31139, + "max_open": 27140, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25811, + "max_open": 21812, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31004, + "max_open": 27005, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30949, + "max_open": 26950, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30856, + "max_open": 26857, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30804, + "max_open": 26805, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25859, + "max_open": 21860, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25714, + "max_open": 21715, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31242, + "max_open": 27243, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30964, + "max_open": 26965, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..0202a58b9173c47b6f4df91b2d0f15c0e47e4161 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_3 (solved pops=79 evals=452 maxopen=374) +[OK ] extrinsic_L0_6 (solved pops=49 evals=312 maxopen=264) +[OK ] extrinsic_L0_5 (solved pops=51 evals=317 maxopen=267) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_8 (solved pops=53 evals=349 maxopen=297) +[OK ] extrinsic_L0_7 (solved pops=55 evals=354 maxopen=300) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=21 evals=167 maxopen=147) +[OK ] extrinsic_L0_9 (solved pops=49 evals=328 maxopen=264) +[OK ] extrinsic_L0_4 (solved pops=221 evals=1217 maxopen=997) +[OK ] extrinsic_L1_4 (solved pops=15 evals=101 maxopen=85) +[OK ] extrinsic_L0_11 (solved pops=217 evals=1186 maxopen=970) +[OK ] extrinsic_L1_1 (solved pops=208 evals=1135 maxopen=910) +[OK ] extrinsic_L1_2 (solved pops=506 evals=2748 maxopen=2243) +[OK ] extrinsic_L1_3 (solved pops=506 evals=2745 maxopen=2240) +[OK ] extrinsic_L2_1 (solved pops=1240 evals=6844 maxopen=5605) +[OK ] extrinsic_L2_6 (solved pops=1664 evals=9794 maxopen=8131) +[OK ] extrinsic_L2_7 (solved pops=998 evals=5694 maxopen=4697) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25995 maxopen=21996) +[OK ] extrinsic_L0_14 (solved pops=3965 evals=25969 maxopen=22005) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25928 maxopen=21929) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25773 maxopen=21774) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25923 maxopen=21924) +[OK ] extrinsic_L2_9 (solved pops=989 evals=5710 maxopen=4722) +[OK ] extrinsic_L2_12 (solved pops=1211 evals=6683 maxopen=5473) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26278 maxopen=22279) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26078 maxopen=22079) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25760 maxopen=21761) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25923 maxopen=21924) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25778 maxopen=21779) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25831 maxopen=21832) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25948 maxopen=21949) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25939 maxopen=21940) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25774 maxopen=21775) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25860 maxopen=21861) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26001 maxopen=22002) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26025 maxopen=22026) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25906 maxopen=21907) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25887 maxopen=21888) +[OK ] extrinsic_L3_14 (solved pops=3124 evals=19429 maxopen=16306) +[OK ] extrinsic_L3_13 (solved pops=3485 evals=22513 maxopen=19029) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25886 maxopen=21887) +[ ] extrinsic_L3_15 (budget pops=4000 evals=25784 maxopen=21785) +[ ] extrinsic_L3_16 (budget pops=4000 evals=25738 maxopen=21739) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25792 maxopen=21793) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25641 maxopen=21642) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25650 maxopen=21651) +[ ] extrinsic_L3_20 (budget pops=4000 evals=25730 maxopen=21731) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25773 maxopen=21774) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25836 maxopen=21837) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26076 maxopen=22077) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26077 maxopen=22078) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26834 maxopen=22835) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25923 maxopen=21924) +[ ] extrinsic_L3_27 (budget pops=4000 evals=25958 maxopen=21959) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25813 maxopen=21814) +[ ] extrinsic_L4_1 (budget pops=4000 evals=25983 maxopen=21984) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26737 maxopen=22738) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26933 maxopen=22934) +[ ] extrinsic_L4_3 (budget pops=4000 evals=25724 maxopen=21725) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25816 maxopen=21817) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26115 maxopen=22116) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25847 maxopen=21848) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26719 maxopen=22720) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26332 maxopen=22333) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25795 maxopen=21796) +[OK ] extrinsic_L4_12 (solved pops=1298 evals=7444 maxopen=6144) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25687 maxopen=21688) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26177 maxopen=22178) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26112 maxopen=22113) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25810 maxopen=21811) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26020 maxopen=22021) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26152 maxopen=22153) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26224 maxopen=22225) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25997 maxopen=21998) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26474 maxopen=22475) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26109 maxopen=22110) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26150 maxopen=22151) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26312 maxopen=22313) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26444 maxopen=22445) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26553 maxopen=22554) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31139 maxopen=27140) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25811 maxopen=21812) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31004 maxopen=27005) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30856 maxopen=26857) +[ ] extrinsic_L6_3 (budget pops=4000 evals=30949 maxopen=26950) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30804 maxopen=26805) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25859 maxopen=21860) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25714 maxopen=21715) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31242 maxopen=27243) +[ ] extrinsic_L6_9 (budget pops=4000 evals=30964 maxopen=26965) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 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'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]].", + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 not_i@type).", + "c em", + "=> (em p1@type).", + "c x2", + "=> (x2 x).", + "a x1", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c x2", + "=> (x2 p3@type@2).", + "c x2", + "=> (x2 goal16).", + "c x2", + "=> (x2 or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5347, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> false]].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal7).", + "intro.", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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(or 'P 'Q)] [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [[[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]] -> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "a or_ir", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]].", + "a x0", + "=> (or [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> 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'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x0", + "=> (x0 exfalso@type and_er@type exfalso and_er).", + "c and_er", + "=> (and_er exfalso@type and_er@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1477, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x goal or_e@type and_el).", + "c x", + "=> (x iff_i@type or_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2035, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A]); [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [false -> ('P : prop) -> 'P]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal16 and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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-> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) (not [('P : prop) -> (not 'P) -> 'P -> false])); [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11938, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> x]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> x]].", + "c x0", + "=> (x0 not_i@type em@type not_i em).", + "c x0", + "=> (x0 and_i@type or_il@type x0 or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type em@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 iff_i@type or_il@type iff_i or_il).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c p8", + "=> (p8 exfalso@type and_i@type exfalso and_i).", + "c x1", + "=> (x1 and_i@type and_i@type p8 and_i).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso and_i).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em x2).", + "c x1", + "=> (x1 iff_er@type iff_i@type iff_er iff_i).", + "c x1", + "=> (x1 goal p11@type and_el p13).", + "c p8", + "=> (p8 p7@type and_i@type p7 p8).", + "c p8", + "=> (p8 p16@type p16@type p16 p16).", + "c x1", + "=> (x1 and_el@type p0@type and_el p0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 532, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not 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[('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))].", + "a x1", + "=> (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]).", + "a x1", + "=> (and (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))])).", + "c em", + "=> (em goal12).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (and (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]))).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x1", + "=> (and x0 [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]).", + "c em", + "=> (em goal22).", + "a x3", + "=> (and [false -> ('P : prop) -> 'P] (and x0 [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]])).", + "a x3", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and [false -> ('P : prop) -> 'P] (and x0 [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]))).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x goal not_i@type and_er).", + "c x", + "=> (x iff_i@type or_il@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1783, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 exfalso@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "c x", + "=> (x p@type p0@type@2 p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 360, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not x); x.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not x)].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso and_er).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1391, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 goal11 goal and_er).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p1@type@2).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 486, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c em", + "=> (em goal7).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a x0", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]].", + "intro.", + "c em", + "=> (em not_i@type).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or false (not false)))]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not (or false (not false)))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 464, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c not_e", + "=> (not_e not_e@type x not_e).", + "intro.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em p0@type).", + "c not_e", + "=> (not_e not_e@type x x0).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> [[('P : prop) -> ('Q : prop) -> 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x goal or_e@type and_i).", + "c x", + "=> (x iff_i@type and_er@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2157, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c x", + "=> (x goal p2@type@2 and_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11059, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> 'B -> (and x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c and_el", + "=> (and_el not_e@type p2@type p3).", + "c x0", + "=> (x0 p0@type exfalso@type p0 exfalso).", + "c x1", + "=> (x1 iff_i@type or_e@type iff_i or_e).", + "c and_el", + "=> (and_el p0@type exfalso@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type goal exfalso x0).", + "c x1", + "=> (x1 exfalso@type p3@type exfalso p3).", + "c x0", + "=> (x0 and_i@type and_er@type x0 and_er).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type goal or_ir x1).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 goal not_e@type and_i not_e).", + "c x1", + "=> (x1 p3@type and_el@type p3 and_el).", + "c x1", + "=> (x1 p13@type p13@type p13 p13).", + "c x0", + "=> (x0 and_er@type goal and_er x1)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2515, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type and_el@type and_el).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal11 em@type em).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 956, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type and_er@type p0 and_er).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p0@type and_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c and_er", + "=> (and_er p0@type and_er@type p3).", + "a exfalso", + "=> false.", + "c p5", + "=> (p5 p0@type and_er@type p3).", + "c p6", + "=> (p6 p0@type and_er@type p3).", + "c em", + "=> (em exfalso@type).", + "a p7", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal10).", + "c p7", + "=> (p7 p0@type and_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a p7", + "=> (and false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]).", + "a p5", + "=> (and (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])).", + "a p7" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 55, + "evals_used": 657, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 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-> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type goal16 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> 'A -> (or 'A 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 635, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (or x 'B)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> (not 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(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1707, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 em@type goal1 em).", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 or_e@type goal or_e or_ir).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el or_e@type goal p6).", + "c and_er", + "=> (and_er or_e@type goal p6).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 508, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> x]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> x].", + "c em", + "=> (em goal8).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p5@type).", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> x]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> x]].", + "a exfalso", + "=> .", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> x]]]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> x]]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> x]]]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> x]]]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] -> [(not [('P : prop) -> (or 'P 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false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or x (not x))).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5721, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (or false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal6).", + "a x1", + "=> (or (not (not [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> (or 'P (not 'P))]); [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_ir", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))])))).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]].", + "c em", + "=> (em goal21).", + "a x1", + "=> (or (not [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]) [[('P : prop) -> (not 'P) -> 'P -> false] -> (or false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]); [(not [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> (or false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x3", + "=> (x3 em).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; 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['Q -> 'R] -> 'R] false); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type p3@type@2 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or (not [[false -> ('P : prop) -> 'P] -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [[false -> ('P : prop) -> 'P] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or (or (not [[false -> ('P : prop) -> 'P] -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [(or (not [[false -> ('P : prop) -> 'P] -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (or (not [[false -> ('P : prop) -> 'P] -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (not [[false -> ('P : prop) -> 'P] -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not false) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not false) -> [false -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [false -> [false -> false]] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 48, + "evals_used": 5174, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type p@type p0 p).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type p4 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il)." + ] + } + ], + "problem": "extrinsic_L0_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 24708, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) 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(iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : 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(or 'P 'Q)]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1936, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c x0", + "=> (x0 or_e@type goal14 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type and_el@type and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : 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'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal13).", + "a 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-> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 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em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2059, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + 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-> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]].", + "a p4", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]].", + "c x2", + "=> (x2 iff_i@type and_i@type iff_i and_i).", + "c x2", + "=> (x2 iff_er@type not_i@type iff_er not_i).", + "a p4", + "=> false.", + "a x3", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c x2", + "=> (x2 and_er@type p6@type and_er p6).", + "c and_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 2888, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + 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false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x goal not_i@type iff_i).", + "c x", + "=> (x iff_i@type or_ir@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1998, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> false].", + "c x", + "=> (x goal p2@type@2 iff_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e p@type x1 p).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p1@type not_e p1).", + "c and_el", + "=> (and_el not_e@type p1@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]] -> false]].", + "c x2", + "=> (x2 exfalso@type p@type exfalso p).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 546, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> 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false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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'R]) -> false].", + "c x", + "=> (x goal goal16 em).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 472, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 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-> false] -> (not 'P)] -> [false -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [false -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_e@type).", + "c x0", + "=> (x0 p3@type@2).", + "a or_e", + "=> [(not x) -> false]; [(not (not x)) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not x) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not x) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10974, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_ir", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal2).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso and_i).", + "c and_er", + "=> (and_er exfalso@type and_i@type p3).", + "c x0", + "=> (x0 x p0@type x2 p0).", + "c p4", + "=> (p4 iff_i@type and_er@type iff_i and_er).", + "c and_er", + "=> (and_er x p0@type p5).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type x exfalso x2).", + "c p4", + "=> (p4 exfalso@type p9@type exfalso p9).", + "c x1", + "=> (x1 and_i@type and_i@type p4 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not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [x -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [x -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x)); (not x).", + "c em", + "=> (em goal11).", + "a not_i", + "=> [(not x) -> false].", + "intro.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + 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prop) -> (or 'A (not 'A))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]])) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]).", + "a x", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) 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(not 'A))]]) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] false)]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] false)]].", + "intro.", + "a x", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> (or 'A (not 'A))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1423, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_ir@type exfalso).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + "evals_used": 7364, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[x -> false] -> (not x)]].", + "a or_e", + 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'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type p@type p0 p).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type p4 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[x -> false] -> (not x)]]]]].", + "c 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-> false]].", + "c x2", + "=> (x2 goal17).", + "a x0", + "=> (iff [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x2", + "=> (x2 goal15)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 918, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> 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false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type em@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 iff_el@type or_ir@type iff_el or_ir).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type p0@type exfalso p0).", + "c p8", + "=> (p8 exfalso@type p6@type exfalso p6).", + "c x1", + "=> (x1 and_i@type and_i@type p8 x0).", + "c x0", + "=> (x0 exfalso@type p6@type exfalso p6).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 or_il@type p0@type or_il p0).", + "c em", + "=> (em x2).", + "c x1", + "=> (x1 em@type exfalso@type em exfalso).", + "c x1", + "=> (x1 p@type p12@type p p12).", + "c p8", + "=> (p8 p6@type p0@type p6 p0).", + "c p8", + "=> (p8 p16@type p11@type p16 p11).", + "c x1", + "=> (x1 and_el@type p15@type and_el p15)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]]) -> false].", + "c x", + "=> (x goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2232, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> 'A -> (not (not 'A))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> 'A -> (not (not 'A))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a not_i", + "=> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> [false -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [false -> [false -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 30, + "evals_used": 1345, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> (not (not x))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> (not (not x))]].", + "c x0", + "=> (x0 not_i@type or_il@type not_i or_il).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_il@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 iff_i@type or_il@type iff_i or_il)." + ] + } + ], + "problem": "extrinsic_L1_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 30666, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + 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false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "c 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> [x -> [(not x) -> 'B]]]] (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])); (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "c not_e", + "=> (not_e exfalso@type x1 x0).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "c x1", + "=> (x1 exfalso@type x0 exfalso).", + "a exfalso", + "=> .", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em goal6).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em or_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7413, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]); [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 em@type goal em x1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x1", + "=> (x1 goal3 and_i@type).", + "c x1", + "=> (x1 goal6 p2@type).", + "c em", + "=> (em goal11).", + "c x1", + "=> (x1 or_ir@type p0@type@2).", + "c x1", + "=> (x1 and_el@type p2@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c and_el", + "=> (and_el em@type goal p1).", + "c p7", + "=> (p7 exfalso@type).", + "c p6", + "=> (p6 and_el).", + "c x1", + "=> (x1 p8@type goal0).", + "c p5", + "=> (p5 or_ir).", + "c x1", + "=> (x1 p11@type em@type).", + "c p10", + "=> (p10 p8).", + "c p7", + "=> (p7 p1@type).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] 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(and 'P 'Q) -> 'Q])) [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]].", + "a x0", + "=> (and [false -> ('P : prop) -> 'P] [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [false -> ('P : prop) -> 'P] [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 357, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "a x1", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [[('P : prop) -> ('Q : prop) -> ['P 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em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1963, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal11).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11199, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "c x0", + "=> (x0 not_i@type or_e@type not_i or_e).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_e@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 iff_el@type p15@type iff_el p15).", + "c x1", + "=> (x1 p@type not_i@type p p5).", + "c p8", + "=> (p8 p7@type exfalso@type p7 exfalso).", + "c p8", + "=> (p8 p16@type p18@type p16 p18).", + "c x1", + "=> (x1 and_el@type iff_el@type and_el iff_el)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4407, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type or_ir@type x).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 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exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6404, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + 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(and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) [false -> ('P : prop) -> 'P]); [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 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-> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + 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-> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q 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'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]]].", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [false -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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['A -> 'C]]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> 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false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])) (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])))]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])) (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2258, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 500, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [false -> ('P : prop) -> 'P]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "intro.", + "intro.", + "a iff_i", + "=> [(and x0 x0) -> x0]; [x0 -> (and x0 x0)].", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]); [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]); [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> false])]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not [[false -> ('P : prop) -> 'P] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> false])]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "a x1", + "=> (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x1", + "=> (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[false -> ('P : prop) -> 'P] -> false]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 392, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]." + ] + }, + { + "mode": "sample", + 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em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> (iff (and 'A 'A) 'A)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> (iff (and 'A 'A) 'A)])).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> (iff (and 'A 'A) 'A)]))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> (iff (and 'A 'A) 'A)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ['P -> false] -> (not 'P)]); [false -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]]); [(or false [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or false [('P : prop) -> ['P -> false] -> (not 'P)])); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (or false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]])]; [(or false [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or (or false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 311, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 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(and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [false -> ('P : prop) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6341, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('A : prop) -> (iff (or 'A 'A) 'A)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]; [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('A : prop) -> (iff (or 'A 'A) 'A)])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('A : prop) -> (iff (or 'A 'A) 'A)])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 309, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a x1", + "=> (iff (not (not false)) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (iff (not (not false)) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (iff (not (not false)) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 619, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "c em", + "=> (em goal0).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not x)); (not x).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not [false -> ('P : prop) -> 'P])); (not 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x and_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 627, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c em", + "=> (em p3@type).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 541, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "intro.", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "a not_i", + "=> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 688, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c and_el", + "=> (and_el x false x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "c em", + "=> (em goal).", + "intro.", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "c em", + "=> (em not_e@type).", + "c and_er", + "=> (and_er x false x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "c em", + "=> (em p2@type).", + "intro.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "intro.", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "c em", + "=> (em p5@type@2).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))).", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))].", + "intro.", + "a x4", + "=> (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))).", + "c x1", + "=> (x1 x false x0).", + "c x2", + "=> (x2 x false x0).", + "c x3", + "=> (x3 x1).", + "a x2", + "=> (and (not [('A : prop) -> (iff (and 'A false) false)]) (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))))).", + "a and_i", + "=> (not [('A : prop) -> (iff (and 'A false) false)]); (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 602, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 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'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a x1", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]].", + "a exfalso", + "=> false.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a x1", + "=> (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1877, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]); [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x or_ir@type iff_el@type or_ir).", + "intro.", + "c iff_er", + "=> (iff_er iff_el@type p5@type@2 p5).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false].", + "c x", + "=> (x exfalso@type or_e@type exfalso).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [false -> false] false); [[false -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [false -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 631, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or false (not false))).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal11).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 585, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3193, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type not_e@type p0 not_e).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p0@type not_e@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c and_er", + "=> (and_er p0@type not_e@type p3).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c x", + "=> (x not_e@type iff_el@type not_e iff_el).", + "c x", + "=> (x iff_el@type em@type iff_el em).", + "c and_er", + "=> (and_er not_e@type iff_el@type p6).", + "c x", + "=> (x em@type iff_i@type em iff_i).", + "c and_el", + "=> (and_el not_e@type iff_el@type p6).", + "c and_el", + "=> (and_el em@type iff_i@type p9).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c p11", + "=> (p11 not_i@type).", + "intro.", + "c and_er", + "=> (and_er em@type iff_i@type p9).", + "intro.", + "c x", + "=> (x or_ir@type p6@type or_ir p6).", + "c p5" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 513, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a iff_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a x0", + "=> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and false (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : 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-> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 305, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a iff_i", + "=> [x -> x]; [x -> x].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 390, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> 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(not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [(or x (not x)) -> false]].", + "a exfalso", + "=> .", + "c em", + "=> (em false).", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3186, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type not_e@type p0 not_e).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p0@type not_e@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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+ "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a x0", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3197, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> 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-> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6510, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]; [false -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]].", + "c em", + "=> 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(or 'P 'Q)] -> false]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]); [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not (or false (not false))) false); [(not (or false (not false))) -> [false -> [false -> false]]]; [false -> [false -> [false -> false]]].", + "a or_il", + "=> (not (or false (not false))).", + "a not_i", + "=> [(or false (not false)) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 617, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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-> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7513, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [false -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] false); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [false -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1054, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c x4", + "=> (x4 goal19 or_ir@type or_ir).", + "intro.", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]).", + "c x0", + "=> (x0 goal11).", + "a not_i", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false].", + "intro.", + "c x0", + "=> (x0 goal10).", + "a or_e", + "=> [[('P : prop) 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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-> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 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(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))) -> false].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 669, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]].", + "a exfalso", + "=> false.", + "a x", + 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)).", + "a x", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)))].", + "intro.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]].", + "a exfalso" + ] + }, + { + "mode": 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))].", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q 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-> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> false]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2255, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em x).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [false -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not false) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c x1", + "=> (x1 not_e@type and_er@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 440, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> 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"=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + 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em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2157, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1053, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c x4", + "=> (x4 goal19 or_ir@type x4).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 565, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", 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['P -> 'Q]])) -> false].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p1@type@2).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> 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prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]; false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x", + "=> (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a x", + "=> (and false (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]] false) false).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and (and [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]] false) false)]; [(not [false -> ('P : prop) -> 'P]) -> (and (and [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]] false) false)].", + "intro.", + "a x0", + "=> false.", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false)]; [(not [false -> ('P : prop) -> 'P]) -> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false)].", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]) -> [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false)]]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]])) -> [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false)]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 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-> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "c em", + "=> (em p3@type).", + "c and_er", + "=> (and_er iff_el@type p0@type p6).", + "c x1", + "=> (x1 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[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]])) -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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: prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c 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-> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [false -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 7508, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8)." + ] + } + ], + "problem": "extrinsic_L3_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 28073, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 166, + "actions": [ + "c em", + "=> (em or_e@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> (not [false -> ('P : prop) -> 'P])]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> (not [false -> ('P : prop) -> 'P])] (not [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> (not [false -> ('P : prop) -> 'P])]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> false] -> false]; [(not [false -> false]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10261, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", 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(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "a and_i", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]].", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]]).", + "a and_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]].", + "a x1", + "=> (and false [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]]).", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and false [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]])).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) false).", + "a x1", + "=> (and [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) false)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 382, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1859, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x0", + "=> (x0 iff_i@type p@type p).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x", + "=> (x p@type p2@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and x [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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: prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 486, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> 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exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 435, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))])))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> (not [false -> ('P : prop) -> 'P])]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[[false -> ('P : prop) -> 'P] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [[false -> ('P : prop) -> 'P] -> false]) (not [[false -> ('P : prop) -> 'P] -> false])); [(not [[false -> ('P : prop) -> 'P] -> false]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [[false -> ('P : prop) -> 'P] -> false]) (not [[false -> ('P : prop) -> 'P] -> false]))]; [(not [false -> ('P : prop) -> 'P]) -> (or (not [[false -> ('P : prop) -> 'P] -> false]) (not [[false -> ('P : prop) -> 'P] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])); (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p1@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + "evals_used": 2042, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 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: prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) false)].", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) false)]; [(and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) false)].", + "a x", + "=> (and [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)))].", + "a or_e" + ] + } + ], + "problem": "extrinsic_L3_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 25705, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> 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false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) 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-> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 637, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", 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'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1405, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]); [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]); [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [false -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false])) (or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]))); [(or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false])) (or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false])) (or [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or false (not false)) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]] -> [[('P : 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 iff_i).", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 705, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (and (not 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+ "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c x4", + "=> (x4 p2@type exfalso@type exfalso).", + "intro.", + "intro.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 574, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 goal11).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))].", + "intro.", + "c not_e", + "=> (not_e em@type x1 em)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 566, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]; false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]).", + "a x", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)]; [(not [false -> ('P : prop) -> 'P]) -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)].", + "intro.", + "a x0", + "=> false.", + "a x", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]])) false).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]])) false)]; [(not [false -> ('P : prop) -> 'P]) -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]])) false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[false -> ('P : prop) -> 'P] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]])) false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[false -> ('P : prop) -> 'P] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]])) false)]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x0", + "=> false.", + "c em" + ] + }, + { + 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or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6578, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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-> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 358, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not false) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not false) -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2376, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e or_il@type x or_il).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> 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not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false].", + "intro.", + "c x2", + "=> (x2 and_i@type p1@type@2 p1).", + "c x2", + "=> (x2 em@type p0@type@2 p0).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x2", + "=> (x2 not_e@type p@type@2 p).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P 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false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]); [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1331, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 674, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : 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-> ['Q -> 'P]])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", 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'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x1", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "intro.", + "c em", + "=> (em p1@type@2).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 634, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [x -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q 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[false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c x1", + "=> (x1 not_e@type or_il@type not_e).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1994, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]].", + "c x2", + "=> (x2 em@type exfalso@type x1 exfalso).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p2@type or_e@type p2 or_e).", + "c x1", + "=> (x1 goal19).", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + 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-> 'R] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7239, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false] -> false]; [(not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false]) -> false].", + "a x", + "=> (or (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false]) (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])); [(not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false]) -> [[[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false] -> false]]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]) -> [[[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false])]].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 666, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])); (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]))]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('A : prop) -> 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-> 'R] -> 'R])]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5657, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> 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['A -> false])]] -> [(not x0) -> [x0 -> false]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]) -> [(not x0) -> [x0 -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])).", + "a exfalso", + "=> false.", + "a x", + "=> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false]))); (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])).", + "c em", + "=> (em goal4).", + "a x1", + "=> (and (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false]))) [false -> ('P : prop) -> 'P]).", + "a and_i", + "=> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]].", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]] [(not x0) -> [x0 -> false]]).", + "a and_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]]; [(not x0) -> [x0 -> false]].", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x1", + "=> (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]] [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false])))]]).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a x1", + "=> (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (iff (not x0) [x0 -> false]))).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 352, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('A : prop) -> (iff (not 'A) ['A -> false])]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2852, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (not 'A) ['A -> false])]].", + "c em", + "=> (em and_el@type).", + "intro.", + "c em", + "=> (em iff_er@type).", + "c x", + "=> (x not_i@type em@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c x", + "=> (x or_il@type false x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x and_i@type goal and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (and [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p2@type iff_el@type p2).", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal11).", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]])].", + "a x1", + "=> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2063, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff (not 'A) ['A -> false])]); [('A : prop) -> (iff (not 'A) ['A -> false])].", + "a not_i", + "=> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c x0", + "=> (x0 or_ir@type iff_i@type or_ir iff_i).", + "c and_el", + "=> (and_el or_ir@type iff_i@type p1).", + "a exfalso", + "=> false.", + "c and_er", + "=> (and_er or_ir@type iff_i@type p1).", + "c p2", + "=> (p2 goal4 goal x1).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not x); x.", + "c x1", + "=> (x1 goal0@1).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p6@type@1 p6@type@2 p6).", + "c iff_er", + "=> (iff_er p6@type@1 p6@type@2 p6).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal0@1).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('A : prop) -> (iff (not 'A) ['A -> false])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "c x0", + "=> (x0 p6@type not_i@type p6 not_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "c x1", + "=> (x1 goal14).", + "c p3", + "=> (p3 p6@type@2 p6@type@1 p8 p7).", + "c and_er" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5660, + "actions": [ + "intro.", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0@1).", + "a or_e", + "=> [(not x) -> false]; [(not (not x)) -> false].", + "a or_e", + "=> [(not x) -> [(not x) -> false]]; [(not (not x)) -> [(not x) -> false]].", + "a or_e", + "=> [(not x) -> [(not x) -> [(not x) -> false]]]; [(not (not x)) -> [(not x) -> [(not x) -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not x) -> [(not x) -> [(not x) -> false]]]); [(not x) -> [(not x) -> [(not x) -> false]]].", + "a not_i", + "=> [[(not x) -> [(not x) -> [(not x) -> false]]] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em x).", + "a not_e", + "=> (not (not [(not x) -> [(not x) -> [(not x) -> false]]])); (not [(not x) -> [(not x) -> [(not x) -> false]]]).", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('A : prop) -> (iff (not 'A) ['A -> false])]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [(not x) -> [(not x) -> [(not x) -> false]]]))]; [[('A : prop) -> (iff (not 'A) ['A -> false])] -> (not (not [(not x) -> [(not x) -> [(not x) -> false]]]))].", + "a or_il", + "=> .", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (not [(not x) -> [(not x) -> [(not x) -> false]]]))).", + "a x0", + "=> (or (not x) (iff (not x) [x -> false])); [(not x) -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (not [(not x) -> [(not x) -> [(not x) -> false]]])))]; [(iff (not x) [x -> false]) -> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (not [(not x) -> [(not x) -> [(not x) -> false]]])))].", + "a x0", + "=> (or [(not x) -> [(not x) -> false]] false); [[(not x) -> [(not x) -> false]] -> (or (not x) (iff (not x) [x -> false]))]; [false -> (or (not x) (iff (not x) [x -> false]))].", + "a or_ir", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[(not x) -> [(not x) -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [(not x) -> [(not x) -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 459, + 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-> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]]; [(not [('A : prop) -> (iff (not 'A) ['A -> false])]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c x0", + "=> (x0 p4@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]]].", + "intro.", + "c iff_el", + "=> (iff_el p6@type@1 p6@type@2 p6).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 509, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff (not 'A) ['A -> 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(not 'A) ['A -> false])])) -> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 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iff_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('A : prop) -> (iff (not 'A) ['A -> false])]) -> false]; [(not (not [('A : prop) -> (iff (not 'A) ['A -> false])])) -> false].", + "c em", + "=> (em p5@type)." + ] + }, + { + "mode": "sample", 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[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]] [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 626, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + 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false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false])); (not [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 goal7 p4@type p6).", + "a not_i", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4214, + "actions": [ + "a 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"=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c x", + "=> (x goal exfalso@type exfalso).", + "c x", + "=> (x p0@type em@type em).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type p@type p).", + "a not_e", + "=> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))); (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not 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-> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "c em", + "=> (em em@type).", + "a x0", + "=> (iff (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a iff_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : 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['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not false) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [false -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not false) -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10229, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a iff_i", + "=> [(and x (or x x2)) -> x]; [x -> (and x (or x x2))].", + "c and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 p@type p2@type p2).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> 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false].", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em not_i@type).", + "intro.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em p6@type).", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 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-> false]]).", + "a and_i", + "=> (not false); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11880, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (not (not x))) -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not (not (not x))) -> (not x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (not (not x))) -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not (not (not x))) -> (not x)]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> 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(iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not false) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [false -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not false) -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [false -> ('P : prop) 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('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))])) -> false]]].", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 873, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "a x1", + 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el iff_el@type p2@type p4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5203, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]]; 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p7@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 457, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q 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-> ['P -> false] -> (not 'P)])])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 328, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 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+ "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c em", + "=> (em p3@type@2).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 552, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]].", + "a x0", + "=> (and (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) (and (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 921, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_er@type p3@type iff_er p3).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el iff_er@type p3@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 503, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 474, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))); (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not (or [('P : prop) -> (not 'P) -> 'P -> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2156, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]] -> false].", + "a x0", + "=> (or (not false) [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]] -> false]); [(not false) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]] -> false]]; [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 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p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1359, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P 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(or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]]].", + "a x2", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]]]].", + "a x2", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]] [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])]; [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])].", + "a x2", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]] [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))])]; [[false -> ('P : prop) -> 'P] -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]] [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))])].", + "c x1", + "=> (x1 p1@type p1@type p1).", + "a x1", + "=> ." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 448, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])); (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x0", + "=> (x0 goal).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or 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+ "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1983, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> 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-> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + 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+ "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not false) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not false); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c iff_el", + "=> (iff_el x x2@type@2 x2).", + "c em", + "=> (em x).", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c x3", + "=> (x3 x x2@type@2 x2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not false) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a x3", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a iff_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [false -> [('P : prop) -> ['P -> false] -> (not 'P)]].", + "a x3", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal7).", + "c em", + "=> (em p8@type).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1326, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type p3@type p3).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false]." + ] + }, + { + "mode": "sample", + 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il" + ] + } + ], + "problem": "extrinsic_L3_26" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 26853, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", 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(not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]).", + "a x1", + "=> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]])).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "a exfalso", + "=> false.", + "a x1", + "=> (and (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]])) false).", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]])) false)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) 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-> (not (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[false -> ('P : prop) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1408, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", 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false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> (or 'P (not 'P))]); [false -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 658, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or false (not 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false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 516, + "actions": [ + "c em", + "=> (em 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or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]]]; [(not [false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]; [(not [false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> [false -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]] -> false]]].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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-> 'P -> false]))])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x2", + "=> (and [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])]] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal22).", + "c x3", + "=> (x3 x1).", + "c p6", + "=> (p6 goal10).", + "c iff_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 917, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x0", + "=> (x0 not_e@type iff_er@type not_e iff_er).", + "c and_er", + "=> (and_er not_e@type iff_er@type p7)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2132, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [x -> (not (not x))]; [(not (not x)) -> x].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x1", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2005, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff x (not (not 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-> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal0@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false]].", + "intro.", + "c x2", + "=> (x2 or_il@type or_il@type or_il or_il).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(iff x (not (not x))) -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(iff x (not (not x))) -> false]].", + "c em", + "=> (em goal0@2@1).", + "c x2", + "=> (x2 p0@type iff_i@type p0 iff_i).", + "c x2", + "=> (x2 p5@type em@type p5 em).", + "c em", + "=> (em or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 381, + "actions": [ + "intro.", + "a iff_i", + "=> [x -> (not (not x))]; [(not (not x)) -> x].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0@2@1).", + "a or_e", + "=> [(not x) -> false]; [(not (not x)) -> false].", + "a or_e", + "=> [(not x) -> [(not x) -> false]]; [(not (not x)) 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 630, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]].", + "c em", + "=> (em 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-> (not 'B)] -> ['B -> 'A]]).", + "a x", + "=> (and (and (and (and (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))))) [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))))) [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> (and (and (and (and (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))))) [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (and [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (and (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false])]].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 882, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> 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"a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal6).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal4).", + "a not_e", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ['P -> false] -> (not 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'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))))].", + "a x1", + "=> (iff (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))) [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x1", + "=> (iff false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x2", + "=> (or (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) x); [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]; [x -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> .", + "a x1", + "=> (iff false (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a iff_i", + "=> [false -> (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))]; [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 518, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x3", + "=> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> (or 'P (not 'P))]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 374, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + 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-> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> 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+ "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]); [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 635, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : 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false)).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)]; [(iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]].", + "intro.", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [false -> [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false).", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em and_er@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 545, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> (and (or false (not false)) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or false (not false)) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and (or false (not false)) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or false (not false)) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or false (not false)) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]].", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or false (not false)) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (or false (not false)) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 346, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p2@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em goal1).", + "c not_e", + "=> (not_e and_i@type x2 and_i).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e and_i@type x2 and_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "a x2", + "=> (and (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 647, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "c x1", + "=> (x1 goal8).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 482, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x iff_i@type p3 iff_i).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3125, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x", + "=> (x p@type@2 p0@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1945, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e p@type x1 p).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1461, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [false -> false] (not false)); [[false -> false] -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]].", + "a or_il", + "=> [false -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_er@type p2 and_er).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 543, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "intro.", + "c x1", + "=> (x1 x0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 em@type).", + "c x1", + "=> (x1 em).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + "evals_used": 6180, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) [('P : prop) -> (not 'P) -> 'P -> false]); [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "a x", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]); [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]]; [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]].", + "a x", + "=> (or (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) -> (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) [('P : prop) -> (not 'P) -> 'P -> false]) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]); [(or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_ir", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "intro.", + "a x", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "c em", + "=> (em goal14).", + "a or_ir" + ] + } + ], + "problem": "extrinsic_L4_5" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 23324, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 166, + "actions": [ + "c em", + "=> (em or_e@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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-> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 p0@type iff_el@type p0 iff_el).", + "c x2", + "=> (x2 em@type iff_i@type em iff_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em goal3).", + "c not_e", + "=> (not_e em@type x em).", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [(not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [false -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1054, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> 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[[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "c em", + "=> (em goal19).", + "c x", + "=> (x not_i@type x3 not_i).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 not_i@type x3 not_i).", + "c x2", + "=> (x2 not_i@type x3 not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 408, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])); (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false] false).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]; false.", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 418, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [x -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not x) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [x -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [x -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type 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-> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + 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-> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]] -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [false -> ('P : 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prop) -> 'P]) -> false]]].", + "c em", + "=> (em goal6).", + "intro.", + "intro.", + "intro.", + "c x3", + "=> (x3 exfalso@type and_er@type exfalso).", + "c x1", + "=> (x1 exfalso@type x4 exfalso).", + "intro.", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "c em", + "=> (em not_i@type).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 513, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a iff_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]); [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p5@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 621, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x", + "=> (x iff_el@type).", + "c x", + "=> (x not_e@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 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prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> 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prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]])]); [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> (not [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]])])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> (not [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]])])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> 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-> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2006, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : 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+ "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [false -> ('P : prop) -> 'P]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> 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or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "c p8", + "=> (p8 goal p1@type p1).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7665, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] -> 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'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 646, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) 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"a x", + "=> (and (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [(and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (and (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a x", + "=> (and [(and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (and (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 536, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> 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[(not (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [(not (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]])]); [(not (not [false -> ('P : prop) -> 'P])) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]])].", + "a exfalso", + "=> false.", + "a x2", + "=> false.", + "a x3", + "=> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 321, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false]; [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])) -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])]; [(not (or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))) -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])].", + "a x", + "=> (not [[(or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])) -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])] -> (not [(or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])) -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])])]).", + "a not_i", + "=> [[[(or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])) -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])] -> (not [(or [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])) -> (not [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])])] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]].", + "c em", + "=> (em and_el@type).", + "intro.", + "c em", + "=> (em iff_er@type).", + "c x", + "=> (x not_i@type em@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c x", + "=> (x or_il@type false x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [false -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x and_i@type goal and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])).", + "a not_i", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c x0", + "=> (x0 not_e@type or_ir@type not_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p3@type or_il@type p3).", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal13).", + "c em", + "=> (em goal11).", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 12601, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [x -> (not x)]) -> x]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [x -> (not x)]) -> x]].", + "intro.", + "a or_e", + 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-> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2156, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> 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goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 362, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : 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'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 664, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x) -> x] -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(not x) -> x] -> x]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x) -> x] -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(not x) -> x] -> x]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a or_e", + "=> [[('P : 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type not_i@type not_i).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2 or_e@type or_e).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p1@type p1@type p1).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 7113, + "actions": [ + "intro.", + "intro.", + "a x0", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [x -> false]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]; [(not [('P : prop) -> 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'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]) -> false].", + "a or_e", + "=> [(not x) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> false]]; [(not (not x)) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> false]].", + "a x1", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> (or 'P (not 'P))] -> [(not x) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not x) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> false]]].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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-> false]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]].", + "intro.", + "c em" + ] + } + ], + "problem": 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-> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + 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-> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1351, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 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: prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 goal8 iff_er@type).", + "a p7", + "=> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c x0", + "=> (x0 goal9 false).", + "c em", + "=> (em p5@type).", + "a p8", + "=> [[[[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false] -> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c x0", + "=> (x0 p4@type p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false] -> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false] -> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 463, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em x).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x1", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6215, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x1", + "=> (x1 or_e@type iff_i@type or_e iff_i).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type iff_i@type p1).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a p4", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [false -> ('P : prop) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [false -> ('P : prop) -> 'P])].", + "a p4", + "=> (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false])); (not [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false]))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]]; [(or (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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false).", + "a exfalso", + "=> false.", + "a x1", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em goal8).", + "intro.", + "a exfalso", + "=> false.", + "a x3", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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'Q]])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x iff_el@type p3 iff_el).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 332, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4270, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_er@type p2 and_er).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 547, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "intro." + ] + }, + { + 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-> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "c em", + "=> (em goal).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x0", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em goal15).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 360, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> (not 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(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 565, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a and_i", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] 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+ "=> (and (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))) (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))))))).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)) -> (and (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))) (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))))]; [(not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) -> (and (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))) (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))))].", + "a x", + "=> (and [('P : prop) -> (or 'P (not 'P))] [(and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)) -> (and (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))) (and (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) (and (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))) (and false (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false).", + "c em", + "=> (em goal9).", + "a and_i", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false); false.", + "a and_i", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false) -> false]; [(not (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 524, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "intro.", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]; [(not (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)])) -> [(not false) -> false]].", + "a or_e", + "=> [false -> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]]; [(not false) -> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> [false -> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [false -> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> [false -> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]]]]; [(not false) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> [false -> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> [false -> [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [(not false) -> false]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> 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-> (and 'P 'Q) -> 'Q]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 iff_i).", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 601, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "intro.", + "a x0", + "=> false.", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type@2).", + "a x3", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (iff [('P : prop) -> (not 'P) -> 'P -> false] false)]; [(not [false -> ('P : prop) -> 'P]) -> (iff [('P : prop) -> (not 'P) -> 'P -> false] false)].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x0", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 434, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]) -> (not [[('P : prop) -> (not 'P) -> 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1333, + "actions": [ + "a exfalso", + "=> false.", + "c em", + 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'B) (and 'A (not 'B))) 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> false].", + "c x0", + "=> (x0 iff_er@type goal11).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P 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-> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1461, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x2", + "=> (x2 or_il@type 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false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 520, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) 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prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])))]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 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prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]; [(not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]].", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]]; [(not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 x).", + "c x1", + "=> (x1 exfalso).", + "c not_e" + ] + }, + { + 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 2367, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (and 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[(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "a exfalso", + "=> false.", + "a x1", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))); [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]; [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "a x1", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))]; [(not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))) -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 376, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not false) -> false]; [(not (not false)) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [(not false) -> false]; [(not (not false)) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> 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-> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]] (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false])))); [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a p4", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[false -> ('P : prop) -> 'P] -> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 714, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 423, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> 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[[[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1892, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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-> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [x -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not x) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]); [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 708, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x2", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))].", + "a x1", + "=> (iff (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false)) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (iff (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false)) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c em", + "=> (em goal11).", + "a x2", + "=> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (iff (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false)) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (iff (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false)) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]].", + "a x2", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]).", + "a x2", + "=> (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]])).", + "a x2", + "=> (and [false -> ('P : prop) -> 'P] (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> (not 'P) -> 'P -> false] false))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]]))).", + "c em", + "=> (em goal19).", + "c em", + "=> (em x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 408, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + 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: prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1339, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em 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'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [false -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> 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-> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 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-> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 644, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(not (iff x x2)) -> (iff x (not x2))]; [(iff x (not x2)) -> (not 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not 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-> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]])]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] -> false]] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + 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'B)))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]]; [(not [[('P : prop) -> (not 'P) -> 'P 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'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_il", + "=> .", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[false -> ('P : prop) -> 'P] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or (not 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) [('P : prop) -> (not 'P) -> 'P -> false]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_il", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "c em", + "=> (em p3@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal15)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 387, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em p2@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x2", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [false -> [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x3", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false).", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 464, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c not_e", + "=> (not_e iff_er@type x0 iff_er).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])); (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [false -> false]].", + "intro.", + "a x0", + "=> (iff false false).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4866, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "c x1", + "=> (x1 exfalso@type goal2 exfalso).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]); [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x1", + "=> (x1 iff_i@type goal2 iff_i).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> false.", + "c x2", + "=> (x2 p4@type exfalso@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 p@type@2 and_i@type).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 440, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal4).", + "a x1", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[false -> ('P : prop) -> 'P] -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[false -> ('P : prop) -> 'P] -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a x1", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x1", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em goal17).", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a x1", + "=> false.", + "a exfalso" + ] + }, + { + "mode": 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[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x p@type em@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 421, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a not_i", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a or_e", + "=> [[(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false] -> false]; [(not [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 453, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not false) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not false) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a iff_i", + "=> [(or (and x (not x2)) (and (not x) x2)) -> (not (iff x x2))]; [(not (iff x x2)) -> (or (and x (not x2)) (and (not x) x2))].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not (iff x x2)) -> (or (and x (not x2)) (and (not x) x2))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not (iff x x2)) -> (or (and x (not x2)) (and (not x) x2))]].", + "a exfalso", + "=> .", + "intro.", + "intro.", + "a exfalso", + "=> .", + "c em", + "=> (em iff_er@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not false) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]].", + "c not_e", + "=> (not_e false x1 x0).", + "c not_e", + "=> (not_e false x1 p3).", + "intro.", + "c em", + "=> (em iff_el@type).", + "c not_e", + "=> (not_e false x1 p4).", + "c x2", + "=> (x2 false x1 x0).", + "a exfalso", + "=> .", + "c em", + "=> (em goal).", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em p5@type@2).", + "c em", + "=> (em or_il@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 557, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x1", + "=> (and false [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (and false [false -> ('P : prop) -> 'P])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (and false [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (and false [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (and false [false -> ('P : prop) -> 'P])]].", + "intro.", + "intro.", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 20, + "evals_used": 159, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not x)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]." + ] + } + ], + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 15, + "evals_used": 27869, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 163, + "actions": [ + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 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prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em goal).", + "a x", + "=> (or false [('P : prop) -> (or 'P (not 'P))]); [false -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p@type).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 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['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or [false -> ('P : prop) -> 'P] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] [false -> ('P : prop) -> 'P]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] 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-> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false])]].", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (not false) (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 443, + "actions": [ + "c em", + "=> (em and_er@type).", + 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: prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6255, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false]))]; [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 621, + 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-> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 452, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false).", + "a and_i", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em em@type).", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)).", + "c em", + "=> (em goal14).", + "a and_i", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)].", + "c em", + "=> (em goal24)." + ] + }, + { + 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p4@type@2).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "intro.", + "a x1", + "=> (iff false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2077, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> false]] -> false]; [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> false]]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5109, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c x2", + "=> (x2 or_il@type and_i@type or_il).", + "c x2", + "=> (x2 p@type iff_er@type p).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x2", + "=> (x2 em@type goal7 em).", + "c em", + "=> (em p3@type).", + "c x2", + "=> (x2 or_il@type x0 x2).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [x0 -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a or_e", + "=> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]; [(not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 p3@type or_ir@type p3).", + "c x2", + "=> (x2 p0@type and_er@type p0).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 416, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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[[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]))]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; 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'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]] false); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])]; [false -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])].", + "a x1", + 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prop) -> ('C : prop) -> [x -> 'B] -> ['B -> 'C] -> ['C -> x] -> (iff x 'B)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> ['B -> 'C] -> ['C -> x] -> (iff x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> ['B -> 'C] -> ['C -> x] -> (iff x 'B)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : 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em", + "=> (em p1@type).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> 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-> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))])))]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))])))]].", + "a exfalso", + "=> false.", + "a x" + ] + } + ], + "problem": "extrinsic_L6_3" + 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false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c x1", + "=> (x1 or_e@type iff_i@type or_e iff_i).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false].", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type iff_i@type p1).", + "a not_i", + "=> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false] -> false].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false] -> false]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a p4", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 406, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))])) -> false] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))])).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))])) -> false]; (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1880, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x", + "=> (x p1@type p1@type p1).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal17).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> 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or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x p0@type p@type p0 p).", + "c and_er", + "=> (and_er p0@type p@type p5).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em not_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 579, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a and_i", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal1).", + "a x", + "=> (and (and false [('P : prop) -> (or 'P (not 'P))]) false).", + "c em", + "=> (em p@type).", + "a x", + "=> (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])).", + "a x", + "=> (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x", + "=> (and (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x", + "=> (and (and (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))])]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> (and (and (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (and [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))])] (and false [('P : prop) -> (or 'P (not 'P))])).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; (and (and (and (and (and false [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ['P -> false] -> (not 'P)]) (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [false -> ('P : prop) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 545, + 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-> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false])]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 965, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x2", + "=> (and (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) false).", + "c em", + "=> (em not_i@type).", + "a x1", + "=> false.", + "c x1", + "=> (x1 exfalso@type iff_el@type exfalso iff_el).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el exfalso@type iff_el@type p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 39, + "evals_used": 97634, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x0", + "=> (x0 goal8 iff_er@type p@type).", + "c x0", + "=> (x0 x goal3 p0@type@2).", + "c x0" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..d244a9d14d41727bcaf87f595d89388d6a9be147 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,875 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_5 (traces=17 evals=21688) +[ ] - extrinsic_L0_3 (traces=17 evals=20295) +[ ] - extrinsic_L0_1 (traces=17 evals=25826) +[ ] - extrinsic_L0_4 (traces=16 evals=25910) +[ ] - extrinsic_L0_6 (traces=13 evals=25174) +[ ] - extrinsic_L0_2 (traces=17 evals=25032) +[OK ] - extrinsic_L0_10 (traces=5 evals=1682) +[ ] - extrinsic_L0_7 (traces=17 evals=24708) + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_11 (traces=17 evals=27517) +[ ] - extrinsic_L0_8 (traces=17 evals=18330) + +thread '' (745220) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false] (x2 [false -> ('P : prop) -> 'P] [('A : prop) -> (not 'A) -> 'A -> false] exfalso not_e)): parameter type (and [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) and value type (and [false -> ('P : prop) -> 'P] [('A : prop) -> (not 'A) -> 'A -> false]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_12 (traces=17 evals=24529) +[ ] - extrinsic_L0_9 (traces=14 evals=24018) +[ ] - extrinsic_L0_13 (traces=13 evals=25468) + +thread '' (745216) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_14 (traces=14 evals=33285) +[ ] - extrinsic_L1_2 (traces=17 evals=30666) +[ ] - extrinsic_L1_1 (traces=13 evals=14181) + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_4 (traces=17 evals=30305) +[ ] - extrinsic_L1_3 (traces=15 evals=32848) +[ ] - extrinsic_L2_1 (traces=13 evals=28713) +[ ] - extrinsic_L2_2 (traces=17 evals=31292) + +thread '' (745213) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (745213) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_6 (traces=17 evals=15370) +[ ] - extrinsic_L2_3 (traces=17 evals=23326) +[ ] - extrinsic_L2_4 (traces=15 evals=20499) +[ ] - extrinsic_L2_5 (traces=8 evals=11333) +[ ] - extrinsic_L2_7 (traces=13 evals=18740) +[ ] - extrinsic_L2_8 (traces=17 evals=17442) +[ ] - extrinsic_L2_10 (traces=17 evals=22676) +[ ] - extrinsic_L2_9 (traces=8 evals=8797) +[ ] - extrinsic_L2_12 (traces=17 evals=21988) +[ ] - extrinsic_L2_11 (traces=17 evals=14082) + +thread '' (745217) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (745217) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745216) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_13 (traces=17 evals=25158) + +thread '' (745216) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745213) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745213) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_1 (traces=17 evals=25306) + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_5 (traces=17 evals=28073) +[ ] - extrinsic_L3_3 (traces=17 evals=21150) +[ ] - extrinsic_L3_2 (traces=8 evals=9785) + +thread '' (745220) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745220) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_4 (traces=13 evals=24563) + +thread '' (745217) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745217) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_6 (traces=15 evals=25142) +[ ] - extrinsic_L3_7 (traces=17 evals=25705) + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_11 (traces=17 evals=19663) +[ ] - extrinsic_L3_8 (traces=15 evals=33794) +[ ] - extrinsic_L3_10 (traces=17 evals=25062) +[ ] - extrinsic_L3_9 (traces=17 evals=22658) +[ ] - extrinsic_L3_12 (traces=17 evals=26469) + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_13 (traces=5 evals=7648) + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_14 (traces=17 evals=22128) +[ ] - extrinsic_L3_17 (traces=17 evals=30969) +[ ] - extrinsic_L3_16 (traces=17 evals=22798) +[ ] - extrinsic_L3_15 (traces=17 evals=34925) +[ ] - extrinsic_L3_18 (traces=17 evals=13621) + +thread '' (745216) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745216) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=16 evals=24533) +[ ] - extrinsic_L3_23 (traces=17 evals=13995) + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_20 (traces=11 evals=9746) +[ ] - extrinsic_L3_21 (traces=15 evals=22463) +[ ] - extrinsic_L3_22 (traces=15 evals=20140) +[ ] - extrinsic_L3_25 (traces=17 evals=16097) +[ ] - extrinsic_L3_24 (traces=17 evals=16007) + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_28 (traces=17 evals=13567) +[ ] - extrinsic_L3_26 (traces=11 evals=10401) +[ ] - extrinsic_L3_27 (traces=17 evals=26853) +[ ] - extrinsic_L3_29 (traces=17 evals=21165) +[ ] - extrinsic_L4_1 (traces=15 evals=27138) +[ ] - extrinsic_L4_2 (traces=17 evals=24644) +[ ] - extrinsic_L4_3 (traces=17 evals=18856) +[ ] - extrinsic_L4_6 (traces=17 evals=23324) +[ ] - extrinsic_L4_4 (traces=15 evals=17649) +[ ] - extrinsic_L4_5 (traces=15 evals=22601) +[ ] - extrinsic_L4_7 (traces=17 evals=23959) +[ ] - extrinsic_L4_8 (traces=11 evals=21176) +[ ] - extrinsic_L4_10 (traces=17 evals=27956) + +thread '' (745141) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_9 (traces=13 evals=25650) + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_11 (traces=13 evals=24901) +[ ] - extrinsic_L4_12 (traces=15 evals=22714) +[ ] - extrinsic_L4_13 (traces=17 evals=18850) +[ ] - extrinsic_L4_14 (traces=12 evals=32707) +[ ] - extrinsic_L5_3 (traces=17 evals=15939) +[ ] - extrinsic_L5_2 (traces=17 evals=16615) +[ ] - extrinsic_L5_1 (traces=8 evals=14205) +[ ] - extrinsic_L5_4 (traces=11 evals=19800) +[ ] - extrinsic_L5_5 (traces=16 evals=25686) +[ ] - extrinsic_L5_7 (traces=17 evals=25524) +[ ] - extrinsic_L5_6 (traces=12 evals=23792) +[ ] - extrinsic_L5_9 (traces=17 evals=17907) +[ ] - extrinsic_L5_8 (traces=13 evals=27819) + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745219) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_10 (traces=15 evals=24735) +[ ] - extrinsic_L5_11 (traces=15 evals=27869) +[ ] - extrinsic_L6_1 (traces=17 evals=22324) +[ ] - extrinsic_L6_3 (traces=8 evals=15077) +[ ] - extrinsic_L6_2 (traces=9 evals=54503) +[ ] - extrinsic_L6_4 (traces=14 evals=16640) +[ ] - extrinsic_L6_5 (traces=8 evals=61401) +[ ] - extrinsic_L6_6 (traces=1 evals=206) +[ ] - extrinsic_L6_7 (traces=2 evals=677) +[ ] - extrinsic_L6_8 (traces=3 evals=40512) +[ ] - extrinsic_L6_9 (traces=6 evals=100751) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 1/94 in 8975.0s diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..4fcb890a03703ddbe29efbb64641d87f8848dce2 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 50 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s46/train.log b/experiments/learnability/train_policy_only/minimo_0pt/s46/train.log new file mode 100644 index 0000000000000000000000000000000000000000..842d4dee535c317ed8d08aa2fbb52a405da9dff4 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s46/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_053034-5gohtf8y +[2026-06-28T05:30:31.306444] Seeded RNGs with seed=46 +[2026-06-28T05:30:31.306747] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-28T05:30:34.797211] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json + 1567 training examples loaded. + +============================================================ +[2026-06-28T05:30:34.799133] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 1567 -> 1567 unique examples + Epoch 1/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 50 total steps, 1567 unique examples (batch_size=64) +[2026-06-28T05:30:45.518762] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:30:45.526257] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s46/2026-06-28_05-30-31/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 50} diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/summary.json b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..c7e0abb57a1d1a8591a555ff44026cabb93c8bd5 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + 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b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..46ae95a33ab973e73e51346544bc2c3e5fe04c8f --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,776 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_8 (solved pops=8 evals=25 maxopen=18) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_7 (solved pops=13 evals=37 maxopen=25) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L1_3 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L1_2 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L0_14 (solved pops=16 evals=62 maxopen=47) +[OK ] extrinsic_L2_1 (solved pops=19 evals=47 maxopen=29) +[OK ] extrinsic_L2_4 (solved pops=14 evals=38 maxopen=25) +[OK ] extrinsic_L2_3 (solved pops=15 evals=60 maxopen=46) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_6 (solved pops=15 evals=33 maxopen=19) +[OK ] extrinsic_L2_8 (solved pops=11 evals=30 maxopen=20) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=12 evals=45 maxopen=34) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L3_1 (solved pops=13 evals=53 maxopen=41) +[OK ] extrinsic_L2_12 (solved pops=45 evals=133 maxopen=89) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L3_2 (solved pops=39 evals=163 maxopen=125) +[OK ] extrinsic_L0_12 (solved pops=106 evals=557 maxopen=435) +[OK ] extrinsic_L2_5 (solved pops=88 evals=381 maxopen=294) +[OK ] extrinsic_L3_4 (solved pops=14 evals=77 maxopen=43) +[OK ] extrinsic_L3_5 (solved pops=14 evals=76 maxopen=42) +[OK ] extrinsic_L3_6 (solved pops=73 evals=250 maxopen=178) +[OK ] extrinsic_L2_2 (solved pops=149 evals=576 maxopen=428) +[OK ] extrinsic_L3_11 (solved pops=115 evals=535 maxopen=418) +[OK ] extrinsic_L3_12 (solved pops=105 evals=504 maxopen=380) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=11 evals=45 maxopen=35) +[OK ] extrinsic_L3_15 (solved pops=79 evals=388 maxopen=310) +[OK ] extrinsic_L3_16 (solved pops=29 evals=89 maxopen=61) +[OK ] extrinsic_L3_17 (solved pops=43 evals=236 maxopen=175) +[OK ] extrinsic_L3_18 (solved pops=33 evals=206 maxopen=153) +[OK ] extrinsic_L3_7 (solved pops=861 evals=4271 maxopen=3411) +[OK ] extrinsic_L3_8 (solved pops=2256 evals=15427 maxopen=13172) +[OK ] extrinsic_L3_10 (solved pops=2788 evals=14601 maxopen=11791) +[ ] extrinsic_L2_13 (budget pops=4000 evals=20259 maxopen=16260) +[OK ] extrinsic_L3_23 (solved pops=47 evals=213 maxopen=167) +[OK ] extrinsic_L3_9 (solved pops=3449 evals=18024 maxopen=14553) +[ ] extrinsic_L3_19 (budget pops=4000 evals=19501 maxopen=15502) +[ ] extrinsic_L3_20 (budget pops=4000 evals=19956 maxopen=15957) +[OK ] extrinsic_L3_25 (solved pops=1165 evals=7941 maxopen=6777) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26033 maxopen=22034) +[ ] extrinsic_L3_21 (budget pops=4000 evals=19864 maxopen=15865) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19355 maxopen=15356) +[ ] extrinsic_L3_27 (budget pops=4000 evals=28464 maxopen=24465) +[ ] extrinsic_L3_26 (budget pops=4000 evals=29577 maxopen=25578) +[ ] extrinsic_L4_1 (budget pops=4000 evals=24247 maxopen=20248) +[ ] extrinsic_L3_28 (budget pops=4000 evals=29941 maxopen=25942) +[ ] extrinsic_L4_2 (budget pops=4000 evals=33704 maxopen=29705) +[OK ] extrinsic_L4_3 (solved pops=1514 evals=9319 maxopen=7806) + +thread '' (4176808) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (4176808) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L4_4 (budget pops=4000 evals=30794 maxopen=26795) +[ ] extrinsic_L3_29 (budget pops=4000 evals=27595 maxopen=23594) +[ ] extrinsic_L4_5 (budget pops=4000 evals=33764 maxopen=29765) +[ ] extrinsic_L4_6 (budget pops=4000 evals=31039 maxopen=27040) +[OK ] extrinsic_L4_12 (solved pops=432 evals=2322 maxopen=1888) +[ ] extrinsic_L4_7 (budget pops=4000 evals=28464 maxopen=24465) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26455 maxopen=22456) +[ ] extrinsic_L4_10 (budget pops=4000 evals=27980 maxopen=23981) +[ ] extrinsic_L4_9 (budget pops=4000 evals=27595 maxopen=23596) +[ ] extrinsic_L4_11 (budget pops=4000 evals=34190 maxopen=30191) +[ ] extrinsic_L4_13 (budget pops=4000 evals=28466 maxopen=24467) +[ ] extrinsic_L4_14 (budget pops=4000 evals=29354 maxopen=25355) +[ ] extrinsic_L5_1 (budget pops=4000 evals=19534 maxopen=15535) +[ ] extrinsic_L5_3 (budget pops=4000 evals=20432 maxopen=16433) +[ ] extrinsic_L5_2 (budget pops=4000 evals=19775 maxopen=15776) + +thread '' (4176722) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L5_6 (budget pops=4000 evals=29235 maxopen=25236) + +thread '' (4176768) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (4176722) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_5 (budget pops=4000 evals=35046 maxopen=31045) +[ ] extrinsic_L5_4 (budget pops=4000 evals=19642 maxopen=15643) +[OK ] extrinsic_L6_1 (solved pops=28 evals=116 maxopen=89) + +thread '' (4176768) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_7 (budget pops=4000 evals=27943 maxopen=23942) +[ ] extrinsic_L5_8 (budget pops=4000 evals=27005 maxopen=23006) +[ ] extrinsic_L5_9 (budget pops=4000 evals=20374 maxopen=16375) +[ ] extrinsic_L5_11 (budget pops=4000 evals=55472 maxopen=51473) +[ ] extrinsic_L5_10 (budget pops=4000 evals=22239 maxopen=18240) +[OK ] extrinsic_L6_6 (solved pops=996 evals=5276 maxopen=4281) +[ ] extrinsic_L6_2 (budget pops=4000 evals=22916 maxopen=18917) +[ ] extrinsic_L6_4 (budget pops=4000 evals=45180 maxopen=41181) +[ ] extrinsic_L6_3 (budget pops=4000 evals=23437 maxopen=19438) +[ ] extrinsic_L6_7 (budget pops=4000 evals=22562 maxopen=18563) +[ ] extrinsic_L6_5 (budget pops=4000 evals=22973 maxopen=18974) +[ ] extrinsic_L6_9 (budget pops=4000 evals=28933 maxopen=24934) +[ ] extrinsic_L6_8 (budget pops=4000 evals=52793 maxopen=48794) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> 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'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A 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prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C 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: prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json +Solved 54/94 in 2312.1s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json new file mode 100644 index 0000000000000000000000000000000000000000..e23d619cb14fe614b20949a91b6b1ba0a3c3cf3f --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json @@ -0,0 +1,1407 @@ +{ + "agent_path": 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"intro.", + "intro.", + "intro.", + "a or_e", + "=> [x -> (or x0 x2)]; [x1 -> (or x0 x2)].", + "intro.", + "a or_il", + "=> x0.", + "a x3", + "=> .", + "intro.", + "a or_ir", + "=> x2.", + "a x4", + "=> ." + ], + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 50535, + "max_open": 46536, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 57828, + "max_open": 53829, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..fddf521b94d96224b89804654db49b094b456a45 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,781 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] 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prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_7 (solved pops=15 evals=42 maxopen=28) +[OK ] extrinsic_L0_8 (solved pops=10 evals=29 maxopen=20) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L0_14 (solved pops=8 evals=26 maxopen=19) +[OK ] extrinsic_L1_3 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L1_2 (solved pops=10 evals=43 maxopen=15) +[OK ] extrinsic_L2_1 (solved pops=23 evals=56 maxopen=34) +[OK ] extrinsic_L2_3 (solved pops=15 evals=60 maxopen=46) +[OK ] extrinsic_L2_4 (solved pops=15 evals=60 maxopen=46) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_8 (solved pops=11 evals=30 maxopen=20) +[OK ] extrinsic_L2_6 (solved pops=19 evals=44 maxopen=26) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=14 evals=50 maxopen=37) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L3_1 (solved pops=13 evals=53 maxopen=41) +[OK ] extrinsic_L0_12 (solved pops=116 evals=650 maxopen=518) +[OK ] extrinsic_L2_5 (solved pops=83 evals=377 maxopen=295) +[OK ] extrinsic_L2_12 (solved pops=58 evals=172 maxopen=115) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L3_2 (solved pops=39 evals=166 maxopen=128) +[OK ] extrinsic_L3_4 (solved pops=17 evals=103 maxopen=66) +[OK ] extrinsic_L3_5 (solved pops=17 evals=84 maxopen=47) +[OK ] extrinsic_L2_2 (solved pops=152 evals=639 maxopen=488) +[OK ] extrinsic_L3_6 (solved pops=90 evals=369 maxopen=280) +[OK ] extrinsic_L3_11 (solved pops=115 evals=532 maxopen=415) +[OK ] extrinsic_L3_12 (solved pops=92 evals=437 maxopen=326) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=13 evals=50 maxopen=38) +[OK ] extrinsic_L3_15 (solved pops=79 evals=345 maxopen=267) +[OK ] extrinsic_L3_16 (solved pops=31 evals=79 maxopen=49) +[OK ] extrinsic_L3_17 (solved pops=47 evals=276 maxopen=211) +[OK ] extrinsic_L3_18 (solved pops=75 evals=514 maxopen=419) +[OK ] extrinsic_L3_7 (solved pops=591 evals=3070 maxopen=2480) +[ ] extrinsic_L2_13 (budget pops=4000 evals=20051 maxopen=16052) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26132 maxopen=22133) +[OK ] extrinsic_L3_10 (solved pops=3928 evals=20622 maxopen=16672) +[OK ] extrinsic_L3_23 (solved pops=42 evals=169 maxopen=128) +[ ] extrinsic_L3_9 (budget pops=4000 evals=21144 maxopen=17145) +[ ] extrinsic_L3_20 (budget pops=4000 evals=18521 maxopen=14522) +[ ] extrinsic_L3_19 (budget pops=4000 evals=18176 maxopen=14177) +[OK ] extrinsic_L3_25 (solved pops=848 evals=5347 maxopen=4480) +[ ] extrinsic_L3_21 (budget pops=4000 evals=18838 maxopen=14839) +[ ] extrinsic_L3_24 (budget pops=4000 evals=22230 maxopen=18231) +[ ] extrinsic_L3_22 (budget pops=4000 evals=18483 maxopen=14484) +[ ] extrinsic_L3_27 (budget pops=4000 evals=28506 maxopen=24507) +[ ] extrinsic_L3_26 (budget pops=4000 evals=28419 maxopen=24420) +[OK ] extrinsic_L4_3 (solved pops=1034 evals=5355 maxopen=4322) +[ ] extrinsic_L3_28 (budget pops=4000 evals=28634 maxopen=24635) + +thread '' (88316) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L4_1 (budget pops=4000 evals=22400 maxopen=18401) +[ ] extrinsic_L4_2 (budget pops=4000 evals=29514 maxopen=25515) + +thread '' (88316) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L4_4 (budget pops=4000 evals=28779 maxopen=24780) + +thread '' (88316) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L4_6 (budget pops=4000 evals=29155 maxopen=25156) +[ ] extrinsic_L4_5 (budget pops=4000 evals=30888 maxopen=26889) +[ ] extrinsic_L3_29 (budget pops=4000 evals=27964 maxopen=23962) +[OK ] extrinsic_L4_12 (solved pops=332 evals=1773 maxopen=1439) +[ ] extrinsic_L4_7 (budget pops=4000 evals=25933 maxopen=21934) +[ ] extrinsic_L4_8 (budget pops=4000 evals=24044 maxopen=20045) +[ ] extrinsic_L4_9 (budget pops=4000 evals=24397 maxopen=20398) +[ ] extrinsic_L4_10 (budget pops=4000 evals=26934 maxopen=22935) +[ ] extrinsic_L4_11 (budget pops=4000 evals=33135 maxopen=29136) +[ ] extrinsic_L4_13 (budget pops=4000 evals=27550 maxopen=23551) +[ ] extrinsic_L4_14 (budget pops=4000 evals=27356 maxopen=23357) +[ ] extrinsic_L5_1 (budget pops=4000 evals=19125 maxopen=15126) + +thread '' (88316) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_2 (budget pops=4000 evals=19894 maxopen=15895) +[ ] extrinsic_L5_3 (budget pops=4000 evals=19457 maxopen=15458) + +thread '' (88315) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L5_6 (budget pops=4000 evals=27042 maxopen=23043) + +thread '' (88316) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (88316) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_5 (budget pops=4000 evals=31046 maxopen=27044) + +thread '' (88315) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_4 (budget pops=4000 evals=19677 maxopen=15678) +[OK ] extrinsic_L6_1 (solved pops=15 evals=40 maxopen=26) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26590 maxopen=22589) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26024 maxopen=22025) +[ ] extrinsic_L5_11 (budget pops=4000 evals=54887 maxopen=50888) +[ ] extrinsic_L5_9 (budget pops=4000 evals=19504 maxopen=15505) +[OK ] extrinsic_L6_6 (solved pops=446 evals=2281 maxopen=1836) +[ ] extrinsic_L5_10 (budget pops=4000 evals=21937 maxopen=17938) +[ ] extrinsic_L6_2 (budget pops=4000 evals=20036 maxopen=16037) +[OK ] extrinsic_L6_7 (solved pops=3817 evals=18832 maxopen=15016) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30163 maxopen=26164) +[ ] extrinsic_L6_3 (budget pops=4000 evals=21024 maxopen=17025) +[ ] extrinsic_L6_5 (budget pops=4000 evals=19986 maxopen=15987) +[ ] extrinsic_L6_9 (budget pops=4000 evals=57828 maxopen=53829) +[ ] extrinsic_L6_8 (budget pops=4000 evals=50535 maxopen=46536) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 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prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "c not_e", + "=> (not_e not_e@type x8 not_e).", + "a x6", + "=> (iff [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal19).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> (iff [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (iff [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em p@type@2).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em goal1).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not x0) -> false]; [(not (not x0)) -> false].", + "a exfalso", + "=> false.", + "a x3", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> false].", + "a x3", + "=> (or [false -> ('P : prop) -> 'P] (not (not x0))); [[false -> ('P : prop) -> 'P] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [[('P : prop) -> 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x5", + "=> (and x0 [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]).", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 p2@type iff_el@type p2).", + "a x5", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] false).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] false)]; [x -> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] false)].", + "c x6", + "=> (x6 not_i@type x0 not_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x6", + "=> (x6 p@type goal12 p).", + "c x4", + "=> (x4 p4@type goal17 p4).", + "c x6", + "=> (x6 x0 goal15 x2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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(iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 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-> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])).", + "a and_i", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]).", + "c em", + "=> (em p4@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 509, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em goal0@1).", + "intro.", + "a not_e", + "=> (not (or [x -> x0] (not [x -> x0]))).", + "a or_e", + "=> [[x -> x0] -> (not (or [x -> x0] (not [x -> x0])))]; [(not [x -> x0]) -> (not (or [x -> x0] (not [x -> x0])))].", + "a or_e", + "=> [[x -> x0] -> [[x -> x0] -> (not (or [x -> x0] (not [x -> x0])))]]; [(not [x -> x0]) -> [[x -> x0] -> (not (or [x -> x0] (not [x -> x0])))]].", + "intro.", + "a or_e", + "=> [[x -> x0] -> [[x -> x0] -> (not (or [x -> x0] (not [x -> x0])))]]; [(not [x -> x0]) -> [[x -> x0] -> (not (or [x -> x0] (not [x -> x0])))]].", + "intro.", + "intro.", + "a not_i", + "=> [(or [x -> x0] (not [x -> x0])) -> false].", + "intro.", + "a or_e", + "=> [[x -> x0] -> false]; [(not [x -> x0]) -> false].", + "c x3", + "=> (x3 or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[x -> x0] -> false]].", + "c x3", + "=> (x3 goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]].", + "c x3", + "=> (x3 goal0@1).", + "c em", + "=> (em goal17).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type@2).", + "intro.", + "a or_e", + "=> [[x -> x0] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]]]; [(not [x -> x0]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[x -> x0] -> false]]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c x3", + "=> (x3 p3@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7153, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "intro.", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [(not [('P : 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false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "intro.", + "c x1", + "=> (x1 or_e@type).", + "c x1", + "=> (x1 p3@type@2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "intro.", + "c em", + "=> (em iff_er@type).", + "c x1", + "=> (x1 p5@type).", + "c x3", + "=> (x3 exfalso@type p3@type false)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..3ea1c36b09f116a381e2462f8737d649b0c97f26 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,870 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_8 (traces=1 evals=30) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] - extrinsic_L0_5 (traces=2 evals=402) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] g extrinsic_L1_2 (traces=1 evals=390) +[OK ] g extrinsic_L1_3 (traces=1 evals=390) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_6 (traces=1 evals=25) +[OK ] g extrinsic_L2_5 (traces=1 evals=43) +[OK ] - extrinsic_L0_9 (traces=2 evals=441) +[OK ] - extrinsic_L1_1 (traces=2 evals=406) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_9 (traces=1 evals=26) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_12 (traces=1 evals=55) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] g extrinsic_L2_13 (traces=1 evals=96) +[OK ] - extrinsic_L3_4 (traces=2 evals=515) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L3_5 (traces=2 evals=587) +[OK ] - extrinsic_L3_2 (traces=3 evals=1048) +[OK ] - extrinsic_L3_9 (traces=5 evals=1681) +[OK ] - extrinsic_L3_1 (traces=14 evals=16891) +[OK ] - extrinsic_L3_11 (traces=3 evals=605) +[ ] - extrinsic_L3_7 (traces=17 evals=10148) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[ ] - extrinsic_L3_10 (traces=17 evals=11505) +[OK ] - extrinsic_L3_14 (traces=4 evals=1553) +[OK ] - extrinsic_L3_12 (traces=8 evals=10913) +[OK ] - extrinsic_L3_17 (traces=2 evals=566) +[OK ] - extrinsic_L3_15 (traces=10 evals=6721) +[OK ] - extrinsic_L3_18 (traces=2 evals=697) +[OK ] - extrinsic_L3_8 (traces=16 evals=18704) + +thread '' (745340) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (745340) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745340) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_2 (traces=17 evals=16140) +[ ] - extrinsic_L3_19 (traces=17 evals=6079) +[OK ] g extrinsic_L3_23 (traces=1 evals=223) + +thread '' (745340) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_16 (traces=17 evals=15755) +[OK ] - extrinsic_L3_24 (traces=13 evals=11128) +[ ] - extrinsic_L3_22 (traces=17 evals=6066) +[ ] - extrinsic_L0_12 (traces=7 evals=19891) +[ ] - extrinsic_L3_20 (traces=17 evals=10532) + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_21 (traces=17 evals=14233) + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_25 (traces=17 evals=9634) + +thread '' (745300) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (745300) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_1 (traces=17 evals=10193) + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_29 (traces=17 evals=12002) + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_26 (traces=17 evals=19452) + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_2 (traces=17 evals=24040) +[ ] - extrinsic_L3_28 (traces=17 evals=21046) +[ ] - extrinsic_L3_27 (traces=17 evals=16404) +[ ] - extrinsic_L4_3 (traces=17 evals=44830) +[ ] - extrinsic_L4_4 (traces=17 evals=37157) +[ ] - extrinsic_L4_8 (traces=17 evals=9208) +[ ] - extrinsic_L4_5 (traces=15 evals=22243) +[ ] - extrinsic_L4_6 (traces=13 evals=34415) +[ ] - extrinsic_L4_7 (traces=15 evals=39446) +[ ] - extrinsic_L4_11 (traces=17 evals=24466) + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_10 (traces=17 evals=37840) +[ ] - extrinsic_L4_12 (traces=17 evals=32576) +[ ] - extrinsic_L4_9 (traces=13 evals=23713) +[ ] - extrinsic_L4_13 (traces=17 evals=24156) +[ ] - extrinsic_L5_2 (traces=17 evals=10480) +[ ] - extrinsic_L5_4 (traces=17 evals=10469) + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745341) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_1 (traces=17 evals=16079) +[ ] - extrinsic_L5_6 (traces=17 evals=7562) +[ ] - extrinsic_L5_3 (traces=17 evals=16686) + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_14 (traces=10 evals=25544) + +thread '' (745300) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745300) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745340) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (745343) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_10 (traces=17 evals=9517) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) +[ ] - extrinsic_L5_7 (traces=17 evals=19185) +[ ] - extrinsic_L5_5 (traces=15 evals=21201) +[ ] - extrinsic_L5_9 (traces=17 evals=12028) +[ ] - extrinsic_L6_5 (traces=17 evals=6085) +[OK ] g extrinsic_L6_6 (traces=1 evals=54) +[ ] - extrinsic_L6_3 (traces=17 evals=10604) +[ ] - extrinsic_L5_11 (traces=11 evals=34365) +[ ] - extrinsic_L5_8 (traces=5 evals=14375) +[ ] - extrinsic_L6_2 (traces=17 evals=11617) + +thread '' (745300) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_8 (traces=17 evals=12746) +[ ] - extrinsic_L6_4 (traces=17 evals=40735) +[ ] - extrinsic_L6_9 (traces=4 evals=79423) +[ ] - extrinsic_L6_7 (traces=14 evals=7929) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 48/94 in 3729.5s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..8ceac5ae3638cd9cec940f240e0028828be0d3d9 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 60 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s42/train.log b/experiments/learnability/train_policy_only/minimo_1pt/s42/train.log new file mode 100644 index 0000000000000000000000000000000000000000..0fc85df8b0193e23e39409c2425ee4cf796daf6e --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s42/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_053035-joytn3an +[2026-06-28T05:30:31.359077] Seeded RNGs with seed=42 +[2026-06-28T05:30:31.359300] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-28T05:30:34.913424] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json + 1880 training examples loaded. + +============================================================ +[2026-06-28T05:30:34.915802] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1880 -> 1880 unique examples + Epoch 1/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 60 total steps, 1880 unique examples (batch_size=64) +[2026-06-28T05:30:47.832009] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:30:47.839337] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s42/2026-06-28_05-30-31/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 60} diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/summary.json b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..3ff0c9406b8b9f836350f5b171763c7a9a2ecf6a --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + 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"/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json" +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..1daacbbbc52faa5735a9f8942f863a9d29be07dc --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json @@ -0,0 +1,1425 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/epoch_2.pt", + "problemset": "extrinsic-95", + "max_pops": 4000, + "max_actions": 0, + "timeout": 600.0, + "workers": 6, + "num_problems": 94, + 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prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_8 (solved pops=8 evals=25 maxopen=18) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_7 (solved pops=15 evals=42 maxopen=28) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_14 (solved pops=10 evals=31 maxopen=22) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_2 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L1_3 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L2_1 (solved pops=15 evals=39 maxopen=25) +[OK ] extrinsic_L2_3 (solved pops=17 evals=65 maxopen=49) +[OK ] extrinsic_L2_4 (solved pops=15 evals=60 maxopen=46) +[OK ] extrinsic_L2_6 (solved pops=15 evals=33 maxopen=19) +[OK ] extrinsic_L2_9 (solved pops=13 evals=31 maxopen=19) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_8 (solved pops=11 evals=30 maxopen=20) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L0_12 (solved pops=85 evals=496 maxopen=395) +[OK ] extrinsic_L3_1 (solved pops=13 evals=53 maxopen=41) +[OK ] extrinsic_L3_3 (solved pops=12 evals=30 maxopen=19) +[OK ] extrinsic_L2_12 (solved pops=38 evals=99 maxopen=62) +[OK ] extrinsic_L3_2 (solved pops=34 evals=136 maxopen=103) +[OK ] extrinsic_L2_5 (solved pops=78 evals=252 maxopen=175) +[OK ] extrinsic_L3_4 (solved pops=16 evals=81 maxopen=45) +[OK ] extrinsic_L3_5 (solved pops=16 evals=80 maxopen=44) +[OK ] extrinsic_L3_6 (solved pops=53 evals=172 maxopen=120) +[OK ] extrinsic_L2_2 (solved pops=146 evals=613 maxopen=468) +[OK ] extrinsic_L3_11 (solved pops=51 evals=217 maxopen=164) +[OK ] extrinsic_L3_12 (solved pops=55 evals=237 maxopen=183) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=11 evals=45 maxopen=35) +[OK ] extrinsic_L3_15 (solved pops=63 evals=272 maxopen=210) +[OK ] extrinsic_L3_16 (solved pops=30 evals=72 maxopen=43) +[OK ] extrinsic_L3_17 (solved pops=42 evals=249 maxopen=189) +[OK ] extrinsic_L3_18 (solved pops=50 evals=330 maxopen=260) +[OK ] extrinsic_L3_7 (solved pops=663 evals=3305 maxopen=2643) +[OK ] extrinsic_L3_10 (solved pops=986 evals=5168 maxopen=4160) +[OK ] extrinsic_L3_9 (solved pops=1115 evals=6296 maxopen=5159) +[OK ] extrinsic_L3_8 (solved pops=2607 evals=16634 maxopen=14028) +[OK ] extrinsic_L3_23 (solved pops=26 evals=118 maxopen=93) +[ ] extrinsic_L2_13 (budget pops=4000 evals=17451 maxopen=13452) +[OK ] extrinsic_L3_25 (solved pops=874 evals=5614 maxopen=4721) +[ ] extrinsic_L3_20 (budget pops=4000 evals=18369 maxopen=14370) +[ ] extrinsic_L3_19 (budget pops=4000 evals=18993 maxopen=14994) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19303 maxopen=15304) +[ ] extrinsic_L3_21 (budget pops=4000 evals=19000 maxopen=15001) +[ ] extrinsic_L3_24 (budget pops=4000 evals=21887 maxopen=17888) + +thread '' (15612) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L4_1 (budget pops=4000 evals=22284 maxopen=18285) + +thread '' (15612) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L4_2 (budget pops=4000 evals=28071 maxopen=24072) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26288 maxopen=22289) +[ ] extrinsic_L3_26 (budget pops=4000 evals=27805 maxopen=23806) + +thread '' (15612) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] extrinsic_L4_3 (solved pops=1609 evals=7933 maxopen=6325) +[ ] extrinsic_L3_28 (budget pops=4000 evals=28660 maxopen=24661) + +thread '' (15612) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (15612) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L3_29 (budget pops=4000 evals=28192 maxopen=24188) +[ ] extrinsic_L4_4 (budget pops=4000 evals=29394 maxopen=25395) +[ ] extrinsic_L4_6 (budget pops=4000 evals=29125 maxopen=25126) +[ ] extrinsic_L4_5 (budget pops=4000 evals=31923 maxopen=27924) +[OK ] extrinsic_L4_12 (solved pops=604 evals=2900 maxopen=2294) +[ ] extrinsic_L4_8 (budget pops=4000 evals=23601 maxopen=19602) +[ ] extrinsic_L4_7 (budget pops=4000 evals=25283 maxopen=21284) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26042 maxopen=22043) +[ ] extrinsic_L4_10 (budget pops=4000 evals=26710 maxopen=22711) +[ ] extrinsic_L4_11 (budget pops=4000 evals=30646 maxopen=26647) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26396 maxopen=22397) +[ ] extrinsic_L4_14 (budget pops=4000 evals=27255 maxopen=23256) +[ ] extrinsic_L5_1 (budget pops=4000 evals=19738 maxopen=15739) + +thread '' (15613) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (15613) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (15613) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (15615) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (15613) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_2 (budget pops=4000 evals=19471 maxopen=15472) +[ ] extrinsic_L5_3 (budget pops=4000 evals=19919 maxopen=15920) + +thread '' (15615) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (15613) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_6 (budget pops=4000 evals=27219 maxopen=23220) + +thread '' (15615) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_5 (budget pops=4000 evals=31080 maxopen=27076) + +thread '' (15615) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_4 (budget pops=4000 evals=19662 maxopen=15663) +[OK ] extrinsic_L6_1 (solved pops=23 evals=57 maxopen=35) + +thread '' (15615) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_7 (budget pops=4000 evals=26275 maxopen=22271) +[ ] extrinsic_L5_11 (budget pops=4000 evals=40607 maxopen=36608) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26242 maxopen=22243) +[ ] extrinsic_L5_9 (budget pops=4000 evals=19220 maxopen=15221) +[OK ] extrinsic_L6_6 (solved pops=664 evals=3429 maxopen=2766) +[ ] extrinsic_L5_10 (budget pops=4000 evals=21759 maxopen=17760) +[ ] extrinsic_L6_2 (budget pops=4000 evals=19696 maxopen=15697) +[ ] extrinsic_L6_4 (budget pops=4000 evals=29593 maxopen=25594) +[ ] extrinsic_L6_7 (budget pops=4000 evals=20187 maxopen=16188) +[ ] extrinsic_L6_3 (budget pops=4000 evals=21036 maxopen=17037) +[ ] extrinsic_L6_5 (budget pops=4000 evals=21076 maxopen=17077) +[ ] extrinsic_L6_9 (budget pops=4000 evals=27666 maxopen=23667) +[ ] extrinsic_L6_8 (budget pops=4000 evals=25865 maxopen=21866) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : 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"intro.", + "intro.", + "intro.", + "intro.", + "c and_er", + "=> (and_er x x1 x5).", + "a and_i", + "=> x0; x2.", + "a x3", + "=> x.", + "c and_el", + "=> (and_el x x1 x5).", + "a x4", + "=> ." + ], + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 23595, + "max_open": 19596, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 50604, + "max_open": 46605, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 61819, + "max_open": 57820, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..38ae76642157325396712d54e29565b93019c310 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_7 (solved pops=12 evals=34 maxopen=23) +[OK ] extrinsic_L0_8 (solved pops=8 evals=25 maxopen=18) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_14 (solved pops=15 evals=44 maxopen=30) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L0_12 (solved pops=36 evals=251 maxopen=199) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_2 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L1_3 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L2_1 (solved pops=23 evals=56 maxopen=34) +[OK ] extrinsic_L2_3 (solved pops=26 evals=132 maxopen=107) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_4 (solved pops=23 evals=108 maxopen=86) +[OK ] extrinsic_L2_8 (solved pops=13 evals=35 maxopen=23) +[OK ] extrinsic_L2_6 (solved pops=19 evals=42 maxopen=24) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=14 evals=50 maxopen=37) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L3_1 (solved pops=24 evals=125 maxopen=102) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L2_12 (solved pops=52 evals=191 maxopen=140) +[OK ] extrinsic_L3_4 (solved pops=20 evals=89 maxopen=49) +[OK ] extrinsic_L3_2 (solved pops=57 evals=300 maxopen=244) +[OK ] extrinsic_L3_5 (solved pops=22 evals=125 maxopen=83) +[OK ] extrinsic_L2_5 (solved pops=99 evals=510 maxopen=412) +[OK ] extrinsic_L2_2 (solved pops=151 evals=707 maxopen=557) +[OK ] extrinsic_L3_6 (solved pops=86 evals=414 maxopen=329) +[OK ] extrinsic_L3_11 (solved pops=94 evals=452 maxopen=356) +[OK ] extrinsic_L3_12 (solved pops=102 evals=509 maxopen=408) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=15 evals=54 maxopen=40) +[OK ] extrinsic_L3_15 (solved pops=101 evals=569 maxopen=469) +[OK ] extrinsic_L3_16 (solved pops=35 evals=103 maxopen=69) +[OK ] extrinsic_L3_17 (solved pops=69 evals=370 maxopen=283) +[OK ] extrinsic_L3_18 (solved pops=65 evals=467 maxopen=382) +[OK ] extrinsic_L3_7 (solved pops=1160 evals=5649 maxopen=4490) +[ ] extrinsic_L2_13 (budget pops=4000 evals=21317 maxopen=17318) +[OK ] extrinsic_L3_9 (solved pops=3167 evals=17639 maxopen=14450) +[ ] extrinsic_L3_10 (budget pops=4000 evals=21557 maxopen=17558) +[OK ] extrinsic_L3_23 (solved pops=58 evals=281 maxopen=224) +[ ] extrinsic_L3_8 (budget pops=4000 evals=29544 maxopen=25545) +[ ] extrinsic_L3_19 (budget pops=4000 evals=21191 maxopen=17192) +[ ] extrinsic_L3_20 (budget pops=4000 evals=20776 maxopen=16777) +[OK ] extrinsic_L3_25 (solved pops=998 evals=7336 maxopen=6319) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19763 maxopen=15764) +[ ] extrinsic_L3_21 (budget pops=4000 evals=21089 maxopen=17090) +[ ] extrinsic_L3_24 (budget pops=4000 evals=28115 maxopen=24116) +[ ] extrinsic_L3_26 (budget pops=4000 evals=28253 maxopen=24254) +[ ] extrinsic_L3_27 (budget pops=4000 evals=29847 maxopen=25848) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26650 maxopen=22651) +[ ] extrinsic_L3_28 (budget pops=4000 evals=27526 maxopen=23527) +[OK ] extrinsic_L4_3 (solved pops=1459 evals=7933 maxopen=6475) +[ ] extrinsic_L4_2 (budget pops=4000 evals=33408 maxopen=29409) +[ ] extrinsic_L4_4 (budget pops=4000 evals=31586 maxopen=27587) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26099 maxopen=22100) +[ ] extrinsic_L4_6 (budget pops=4000 evals=31925 maxopen=27926) +[ ] extrinsic_L4_5 (budget pops=4000 evals=35260 maxopen=31261) +[OK ] extrinsic_L4_12 (solved pops=371 evals=1883 maxopen=1510) +[ ] extrinsic_L4_7 (budget pops=4000 evals=28342 maxopen=24343) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26859 maxopen=22860) +[ ] extrinsic_L4_9 (budget pops=4000 evals=29424 maxopen=25425) +[ ] extrinsic_L4_10 (budget pops=4000 evals=30691 maxopen=26692) +[ ] extrinsic_L4_13 (budget pops=4000 evals=30966 maxopen=26967) +[ ] extrinsic_L4_11 (budget pops=4000 evals=37739 maxopen=33740) +[ ] extrinsic_L4_14 (budget pops=4000 evals=31514 maxopen=27515) +[ ] extrinsic_L5_1 (budget pops=4000 evals=21174 maxopen=17175) +[ ] extrinsic_L5_2 (budget pops=4000 evals=22089 maxopen=18090) +[ ] extrinsic_L5_3 (budget pops=4000 evals=22114 maxopen=18115) +[ ] extrinsic_L5_6 (budget pops=4000 evals=28897 maxopen=24898) +[ ] extrinsic_L5_4 (budget pops=4000 evals=21263 maxopen=17264) +[ ] extrinsic_L5_5 (budget pops=4000 evals=31486 maxopen=27487) +[OK ] extrinsic_L6_1 (solved pops=42 evals=243 maxopen=202) +[ ] extrinsic_L5_7 (budget pops=4000 evals=27811 maxopen=23812) +[ ] extrinsic_L5_8 (budget pops=4000 evals=29075 maxopen=25076) +[ ] extrinsic_L5_9 (budget pops=4000 evals=20719 maxopen=16720) +[ ] extrinsic_L5_10 (budget pops=4000 evals=23518 maxopen=19519) +[ ] extrinsic_L5_11 (budget pops=4000 evals=81717 maxopen=77718) +[OK ] extrinsic_L6_6 (solved pops=1513 evals=7540 maxopen=6028) +[ ] extrinsic_L6_2 (budget pops=4000 evals=22775 maxopen=18776) +[ ] extrinsic_L6_4 (budget pops=4000 evals=44941 maxopen=40942) +[ ] extrinsic_L6_3 (budget pops=4000 evals=23600 maxopen=19601) +[ ] extrinsic_L6_5 (budget pops=4000 evals=23075 maxopen=19076) +[ ] extrinsic_L6_7 (budget pops=4000 evals=23595 maxopen=19596) +[ ] extrinsic_L6_9 (budget pops=4000 evals=61819 maxopen=57820) +[ ] extrinsic_L6_8 (budget pops=4000 evals=50604 maxopen=46605) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 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[(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 52/94 in 2411.7s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..8be8dc1a03d98f0a83d105c31c1fea3752ca0c53 --- /dev/null +++ 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-> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false))))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false))) (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and (and 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "c em", + "=> (em goal4).", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "c em", + "=> (em goal0).", + "intro.", + "c not_e", + "=> (not_e or_ir@type x3 or_ir).", + "a or_il", + "=> .", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a x2", + "=> (or false x0); [false -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]]; [x0 -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]].", + "a x2", + "=> (or [('P : prop) -> (or 'P (not 'P))] [x -> x0]); [[('P : prop) -> (or 'P (not 'P))] -> (or false x0)]; [[x -> x0] -> (or false x0)].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] [x -> x0])]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [('P : prop) -> (or 'P (not 'P))] [x -> x0])].", + "a x2", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] [x -> x0])]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] [x -> x0])]].", + "a or_ir", + "=> .", + "intro.", + 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[[[[x -> x0] -> x] -> x] -> [[[[x -> x0] -> x] -> x] -> false]]].", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not (not x)) [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (not (not x)) [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])].", + "a or_e", + "=> [[[[x -> x0] -> x] -> x] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[[x -> x0] -> x] -> x]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (or false (or (not (not x)) (not (not (not x))))); [false -> [[[[x -> x0] -> x] -> x] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(or (not (not x)) (not (not (not x)))) -> [[[[x -> x0] -> x] -> x] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_ir", + "=> .", + "intro.", + "a x2", + "=> (or (or (not (not x)) [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not x))]); [(or (not (not x)) [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> [[[[x -> x0] -> x] -> x] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not x))] -> [[[[x -> x0] -> x] -> x] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a x1", + "=> (or [[[[x -> x0] -> x] -> x] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])] [('P : prop) -> ('Q : prop) -> (iff 'P 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-> x]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal13).", + "a x2", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and false false) (iff (not [x -> x0]) (and x (not x0))))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x]) [('P : prop) -> ['P -> false] -> (not 'P)]) [x -> x0]).", + "c em", + "=> (em or_il@type).", + "c not_e", + "=> (not_e and_el@type x3 and_el).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and false false) (iff (not [x -> x0]) (and x (not x0))))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x]) [('P : prop) -> ['P -> false] -> (not 'P)]) [x -> x0])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and false false) (iff (not [x -> x0]) (and x (not x0))))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a x2", + "=> (and (iff x (iff x0 x1)) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (iff x (iff x0 x1)) false)].", + "a x3", + "=> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])].", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])]).", + "a x4", + "=> (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])])).", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])]))).", + "c em", + "=> (em goal11).", + "a x4", + "=> (and (and (iff x (iff x0 x1)) false) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])])))).", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and (iff x (iff x0 x1)) false) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])]))))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and (iff x (iff x0 x1)) false) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])])))))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and (iff x (iff x0 x1)) false) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])])))))].", + "a x2", + "=> (and x [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and (iff x (iff x0 x1)) false) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])])))))]).", + "c em", + "=> (em or_il@type).", + "a x2", + "=> (and (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])])) (and x [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and (iff x (iff x0 x1)) false) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (iff (iff x (iff x0 x1)) (iff (iff x x0) x1)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (iff x (iff x0 x1)) false)])])))))]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 274, + "actions": [ + "intro.", + "intro.", + "intro.", + "a iff_i", + "=> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]; [(iff (iff x x0) x1) -> (iff x (iff x0 x1))].", + "intro.", + "c iff_er", + "=> (iff_er x goal0@1@2 x2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el x goal0@1@2 x2).", + "a not_e", + "=> (not (iff (iff x x0) x1)); (iff (iff x x0) x1).", + "a not_i", + "=> [(iff (iff x x0) x1) -> false].", + "intro.", + "c iff_el", + "=> (iff_el goal0@2@1 x1 x3).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x6", + "=> (iff false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x6", + "=> (iff false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c iff_er", + "=> (iff_er goal0@2@1 x1 x3).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x6", + "=> (x6 x goal0@1@2 x2).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 518, + "actions": [ + "intro.", + "intro.", + "intro.", + "a iff_i", + "=> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]; [(iff (iff x x0) x1) -> (iff x (iff x0 x1))].", + "intro.", + "c iff_er", + "=> (iff_er x goal0@1@2 x2).", + "a iff_i", + "=> [(iff x x0) -> x1]; [x1 -> (iff x x0)].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(iff x0 x1) -> x]).", + "a not_i", + "=> [[(iff x0 x1) -> x] -> false].", + "intro.", + "a 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"intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])]); [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])].", + "a not_i", + "=> [[[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] -> false].", + "c x4", + "=> (x4 and_er@type iff_i@type and_er iff_i).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x5", + "=> (x5 x2).", + "c x4", + "=> (x4 iff_i@type goal0 iff_i x5).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c x4", + "=> (x4 not_i@type x0 not_i x3).", + "c em", + "=> (em goal).", + "c and_er", + "=> (and_er and_er@type iff_i@type p).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c and_el", + "=> (and_el iff_i@type goal0 p1).", + "c em", + "=> (em goal1@2).", + "a or_e", + "=> [x -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[x0 -> x1] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c and_er", + "=> (and_er not_i@type x0 p2).", + "c em", + "=> (em p2@type).", + "c and_el", + "=> (and_el and_er@type iff_i@type p).", + "c and_el", + "=> (and_el not_i@type x0 p2).", + "a exfalso", + "=> false.", + "a p9" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 383, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x4", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "a x4", + "=> (not x1); x1.", + "a not_i", + "=> [x1 -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x4", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "intro.", + "a x4", + "=> (not [x -> false]); [x -> false].", + "a not_i", + "=> [[x -> false] -> false].", + "intro.", + "a x8", + "=> .", + "intro.", + "a not_e", + "=> (not [x1 -> false]); [x1 -> false].", + "a exfalso", + "=> false.", + "a x6", + "=> (not [(or x x0) -> (or x x1)]).", + "a not_i", + "=> [[(or x x0) -> (or x x1)] -> false].", + "intro.", + "a not_e", + "=> (not (not x)); (not x).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or x x0) -> (or x x1)]).", + "a not_i", + "=> [[(or x x0) -> (or x x1)] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x5", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x6", + "=> false.", + "a x5", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x6", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0).", + "a not_i", + "=> [x0 -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x5", + "=> (not [x0 -> false]); [x0 -> false].", + "a not_i", + "=> [[x0 -> false] -> false].", + "intro.", + "c x8", + "=> (x8 x7).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a x6", + "=> false.", + "a not_e", + "=> (not [(or x x0) -> (or x x1)]).", + "a not_i", + "=> [[(or x x0) -> (or x x1)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 54, + "evals_used": 83091, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false].", + "intro.", + "c x", + "=> (x or_il@type goal or_il).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "c x0", + "=> (x0 goal7 iff_i@type goal6).", + "a x1", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]).", + "c em", + "=> (em p@type).", + "c x", + "=> (x or_il@type goal10 x).", + "c x0", + "=> (x0 iff_i@type goal3 iff_el@type).", + "a x1", + "=> false.", + "c x0", + "=> (x0 false iff_el@type and_i@type).", + "c x", + "=> (x not_i@type goal not_i).", + "c em", + "=> (em or_ir@type).", + "a x1", + "=> false.", + "c x", + "=> (x iff_el@type goal10 iff_el).", + "a x1", + "=> false.", + "c x0", + "=> (x0 goal3 goal3 not_i@type)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..c0c4cfeac51296f73e3f23dd55c46e430cc3ec3a --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,911 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_8 (traces=1 evals=30) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] g extrinsic_L1_2 (traces=1 evals=19) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L1_3 (traces=1 evals=19) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] - extrinsic_L0_5 (traces=2 evals=404) +[OK ] - extrinsic_L0_9 (traces=2 evals=442) +[OK ] - extrinsic_L1_1 (traces=2 evals=409) +[OK ] g extrinsic_L2_5 (traces=1 evals=48) +[OK ] g extrinsic_L2_6 (traces=1 evals=25) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] - extrinsic_L2_3 (traces=2 evals=490) +[OK ] g extrinsic_L2_9 (traces=1 evals=26) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_12 (traces=1 evals=55) +[OK ] - extrinsic_L2_4 (traces=2 evals=561) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L3_4 (traces=2 evals=613) +[OK ] - extrinsic_L2_13 (traces=3 evals=710) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L3_5 (traces=3 evals=1104) +[OK ] - extrinsic_L3_2 (traces=10 evals=4248) + +thread '' (870070) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870071) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870071) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_2 (traces=17 evals=10474) +[OK ] - extrinsic_L3_1 (traces=11 evals=15087) +[OK ] - extrinsic_L3_11 (traces=3 evals=1097) +[OK ] - extrinsic_L3_12 (traces=8 evals=2484) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[ ] - extrinsic_L3_8 (traces=17 evals=9384) +[ ] - extrinsic_L3_7 (traces=17 evals=12550) +[OK ] - extrinsic_L3_14 (traces=4 evals=1635) +[OK ] - extrinsic_L3_15 (traces=4 evals=1400) +[OK ] - extrinsic_L3_18 (traces=2 evals=577) +[ ] - extrinsic_L3_9 (traces=17 evals=10150) +[OK ] - extrinsic_L3_16 (traces=5 evals=1984) +[OK ] - extrinsic_L3_17 (traces=7 evals=4672) +[OK ] - extrinsic_L3_10 (traces=7 evals=6892) +[OK ] g extrinsic_L3_23 (traces=1 evals=33) +[ ] - extrinsic_L3_20 (traces=17 evals=5673) + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=17 evals=8025) +[ ] - extrinsic_L3_21 (traces=17 evals=5989) + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L3_24 (traces=16 evals=14832) +[ ] - extrinsic_L3_22 (traces=17 evals=8911) + +thread '' (870070) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870065) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_25 (traces=17 evals=8494) + +thread '' (870071) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_12 (traces=7 evals=20094) +[ ] - extrinsic_L4_2 (traces=17 evals=21537) +[ ] - extrinsic_L3_28 (traces=17 evals=8221) +[OK ] - extrinsic_L3_27 (traces=16 evals=15629) +[ ] - extrinsic_L3_26 (traces=17 evals=32416) +[ ] - extrinsic_L3_29 (traces=17 evals=25456) +[ ] - extrinsic_L4_3 (traces=17 evals=21122) +[ ] - extrinsic_L4_1 (traces=15 evals=15701) +[ ] - extrinsic_L4_6 (traces=17 evals=24293) +[ ] - extrinsic_L4_7 (traces=17 evals=16485) +[ ] - extrinsic_L4_8 (traces=17 evals=7595) + +thread '' (870070) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870070) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_9 (traces=17 evals=19075) +[ ] - extrinsic_L4_4 (traces=15 evals=19430) +[ ] - extrinsic_L4_5 (traces=7 evals=15518) +[ ] - extrinsic_L5_1 (traces=17 evals=10572) +[ ] - extrinsic_L4_10 (traces=15 evals=29359) +[ ] - extrinsic_L4_11 (traces=15 evals=28882) +[ ] - extrinsic_L4_12 (traces=17 evals=15904) + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870070) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_2 (traces=17 evals=9180) +[ ] - extrinsic_L5_3 (traces=17 evals=7830) +[ ] - extrinsic_L4_13 (traces=15 evals=38908) +[ ] - extrinsic_L5_4 (traces=17 evals=11265) + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870071) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_14 (traces=16 evals=29440) + +thread '' (870065) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870065) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870071) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870071) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870071) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870065) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870065) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_7 (traces=17 evals=17262) + +thread '' (870068) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_5 (traces=17 evals=15905) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) +[ ] - extrinsic_L5_8 (traces=17 evals=10938) + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_10 (traces=17 evals=6388) + +thread '' (870069) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870069) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=17 evals=8650) +[ ] - extrinsic_L5_6 (traces=17 evals=21608) +[OK ] g extrinsic_L6_6 (traces=1 evals=63) + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_7 (traces=17 evals=10153) +[ ] - extrinsic_L6_2 (traces=17 evals=8212) +[ ] - extrinsic_L6_5 (traces=17 evals=6012) + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870072) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_11 (traces=17 evals=27623) +[ ] - extrinsic_L6_4 (traces=17 evals=14705) +[ ] - extrinsic_L6_8 (traces=17 evals=12708) +[ ] - extrinsic_L6_3 (traces=5 evals=6131) +[ ] - extrinsic_L6_9 (traces=13 evals=98062) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 49/94 in 3268.2s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..8ceac5ae3638cd9cec940f240e0028828be0d3d9 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 60 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s43/train.log b/experiments/learnability/train_policy_only/minimo_1pt/s43/train.log new file mode 100644 index 0000000000000000000000000000000000000000..8d95240e0a198e1c4f9c0a1eb0aa79ee324e335e --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s43/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_053054-wuicmat5 +[2026-06-28T05:30:50.775360] Seeded RNGs with seed=43 +[2026-06-28T05:30:50.775646] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-28T05:30:54.182520] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json + 1880 training examples loaded. + +============================================================ +[2026-06-28T05:30:54.185368] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1880 -> 1880 unique examples + Epoch 1/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 60 total steps, 1880 unique examples (batch_size=64) +[2026-06-28T05:31:07.247726] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:31:07.255736] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s43/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 60} diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/summary.json b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..7aa622a374f6f2699f5db38311547851c40df47d --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_1_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 60 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/ablation_config.json b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/ablation_config.json new file mode 100644 index 0000000000000000000000000000000000000000..ef9839e91529f242f0fa0d586a563f31e425e03e --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/ablation_config.json @@ -0,0 +1,8 @@ +{ + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1, + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": 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mode 100644 index 0000000000000000000000000000000000000000..693858fe9157ef4c2b64671abc6ee2e60f3ca848 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,779 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : 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(or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) +[OK ] extrinsic_L0_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_8 (solved pops=6 evals=19 maxopen=14) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_7 (solved pops=10 evals=28 maxopen=19) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L1_2 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_3 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L0_14 (solved pops=18 evals=67 maxopen=50) +[OK ] extrinsic_L2_1 (solved pops=17 evals=43 maxopen=27) +[OK ] extrinsic_L2_4 (solved pops=19 evals=68 maxopen=50) +[OK ] extrinsic_L2_3 (solved pops=22 evals=92 maxopen=71) +[OK ] extrinsic_L2_6 (solved pops=15 evals=33 maxopen=19) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_8 (solved pops=13 evals=35 maxopen=23) +[OK ] extrinsic_L2_9 (solved pops=14 evals=50 maxopen=37) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L0_12 (solved pops=74 evals=367 maxopen=277) +[OK ] extrinsic_L3_1 (solved pops=21 evals=103 maxopen=83) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L2_12 (solved pops=42 evals=124 maxopen=83) +[OK ] extrinsic_L2_5 (solved pops=85 evals=355 maxopen=271) +[OK ] extrinsic_L3_4 (solved pops=19 evals=107 maxopen=68) +[OK ] extrinsic_L3_5 (solved pops=19 evals=105 maxopen=66) +[OK ] extrinsic_L3_2 (solved pops=48 evals=241 maxopen=194) +[OK ] extrinsic_L3_6 (solved pops=70 evals=258 maxopen=189) +[OK ] extrinsic_L2_2 (solved pops=152 evals=590 maxopen=439) +[OK ] extrinsic_L3_11 (solved pops=87 evals=367 maxopen=278) +[OK ] extrinsic_L3_12 (solved pops=91 evals=425 maxopen=315) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=11 evals=45 maxopen=35) +[OK ] extrinsic_L3_15 (solved pops=88 evals=441 maxopen=354) +[OK ] extrinsic_L3_16 (solved pops=31 evals=95 maxopen=65) +[OK ] extrinsic_L3_17 (solved pops=45 evals=256 maxopen=193) +[OK ] extrinsic_L3_18 (solved pops=47 evals=305 maxopen=238) +[OK ] extrinsic_L3_7 (solved pops=1022 evals=4914 maxopen=3893) +[OK ] extrinsic_L3_8 (solved pops=2073 evals=13824 maxopen=11752) +[OK ] extrinsic_L3_10 (solved pops=2358 evals=12196 maxopen=9816) +[OK ] extrinsic_L3_9 (solved pops=2497 evals=13408 maxopen=10889) +[OK ] extrinsic_L3_23 (solved pops=45 evals=189 maxopen=145) +[ ] extrinsic_L2_13 (budget pops=4000 evals=19340 maxopen=15341) +[OK ] extrinsic_L3_25 (solved pops=1103 evals=7422 maxopen=6300) +[ ] extrinsic_L3_19 (budget pops=4000 evals=19756 maxopen=15757) +[ ] extrinsic_L3_20 (budget pops=4000 evals=19910 maxopen=15911) +[ ] extrinsic_L3_24 (budget pops=4000 evals=24198 maxopen=20199) +[ ] extrinsic_L3_21 (budget pops=4000 evals=19741 maxopen=15742) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19842 maxopen=15843) +[ ] extrinsic_L4_1 (budget pops=4000 evals=24163 maxopen=20164) +[ ] extrinsic_L3_26 (budget pops=4000 evals=28804 maxopen=24805) +[ ] extrinsic_L3_27 (budget pops=4000 evals=27104 maxopen=23105) +[ ] extrinsic_L4_2 (budget pops=4000 evals=32718 maxopen=28719) +[ ] extrinsic_L3_28 (budget pops=4000 evals=30335 maxopen=26336) + +thread '' (16013) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] extrinsic_L4_3 (solved pops=1776 evals=11669 maxopen=9894) + +thread '' (16013) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (16013) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L4_4 (budget pops=4000 evals=30489 maxopen=26490) +[ ] extrinsic_L3_29 (budget pops=4000 evals=28129 maxopen=24127) +[ ] extrinsic_L4_5 (budget pops=4000 evals=32242 maxopen=28243) +[ ] extrinsic_L4_6 (budget pops=4000 evals=29919 maxopen=25920) +[OK ] extrinsic_L4_12 (solved pops=576 evals=3266 maxopen=2688) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26924 maxopen=22925) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26985 maxopen=22986) +[ ] extrinsic_L4_10 (budget pops=4000 evals=27780 maxopen=23781) +[ ] extrinsic_L4_9 (budget pops=4000 evals=27536 maxopen=23537) +[ ] extrinsic_L4_11 (budget pops=4000 evals=33417 maxopen=29418) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26972 maxopen=22973) +[ ] extrinsic_L4_14 (budget pops=4000 evals=28613 maxopen=24614) +[ ] extrinsic_L5_1 (budget pops=4000 evals=19624 maxopen=15625) +[ ] extrinsic_L5_3 (budget pops=4000 evals=20132 maxopen=16133) +[ ] extrinsic_L5_2 (budget pops=4000 evals=19752 maxopen=15753) +[ ] extrinsic_L5_6 (budget pops=4000 evals=27751 maxopen=23752) + +thread '' (16009) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (16009) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (16011) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L5_5 (budget pops=4000 evals=31405 maxopen=27404) +[ ] extrinsic_L5_4 (budget pops=4000 evals=19641 maxopen=15642) +[OK ] extrinsic_L6_1 (solved pops=32 evals=162 maxopen=131) + +thread '' (16011) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_7 (budget pops=4000 evals=25866 maxopen=21865) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26378 maxopen=22379) +[ ] extrinsic_L5_11 (budget pops=4000 evals=40858 maxopen=36859) +[ ] extrinsic_L5_9 (budget pops=4000 evals=20341 maxopen=16342) +[OK ] extrinsic_L6_6 (solved pops=1214 evals=6469 maxopen=5256) +[ ] extrinsic_L5_10 (budget pops=4000 evals=21954 maxopen=17955) +[ ] extrinsic_L6_2 (budget pops=4000 evals=22496 maxopen=18497) +[ ] extrinsic_L6_4 (budget pops=4000 evals=27934 maxopen=23935) +[ ] extrinsic_L6_3 (budget pops=4000 evals=22783 maxopen=18784) +[ ] extrinsic_L6_7 (budget pops=4000 evals=23247 maxopen=19248) +[ ] extrinsic_L6_5 (budget pops=4000 evals=23035 maxopen=19036) +[ ] extrinsic_L6_9 (budget pops=4000 evals=27521 maxopen=23522) +[ ] extrinsic_L6_8 (budget pops=4000 evals=27722 maxopen=23723) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A 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b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,763 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_8 (solved pops=12 evals=34 maxopen=23) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L0_7 (solved pops=19 evals=53 maxopen=35) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_2 (solved pops=10 evals=43 maxopen=15) +[OK ] extrinsic_L0_14 (solved pops=10 evals=31 maxopen=22) +[OK ] extrinsic_L1_3 (solved pops=10 evals=43 maxopen=15) +[OK ] extrinsic_L2_4 (solved pops=13 evals=55 maxopen=43) +[OK ] extrinsic_L2_1 (solved pops=25 evals=62 maxopen=38) +[OK ] extrinsic_L2_3 (solved pops=21 evals=73 maxopen=53) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_8 (solved pops=11 evals=30 maxopen=20) +[OK ] extrinsic_L2_6 (solved pops=21 evals=49 maxopen=29) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=14 evals=50 maxopen=37) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L0_12 (solved pops=81 evals=431 maxopen=334) +[OK ] extrinsic_L3_1 (solved pops=23 evals=75 maxopen=53) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L2_5 (solved pops=93 evals=468 maxopen=376) +[OK ] extrinsic_L2_12 (solved pops=62 evals=216 maxopen=155) +[OK ] extrinsic_L3_4 (solved pops=19 evals=107 maxopen=68) +[OK ] extrinsic_L3_5 (solved pops=19 evals=105 maxopen=66) +[OK ] extrinsic_L3_2 (solved pops=58 evals=292 maxopen=235) +[OK ] extrinsic_L3_6 (solved pops=94 evals=446 maxopen=353) +[OK ] extrinsic_L2_2 (solved pops=172 evals=709 maxopen=538) +[OK ] extrinsic_L3_11 (solved pops=92 evals=435 maxopen=341) +[OK ] extrinsic_L3_12 (solved pops=69 evals=308 maxopen=220) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=13 evals=50 maxopen=38) +[OK ] extrinsic_L3_15 (solved pops=85 evals=394 maxopen=310) +[OK ] extrinsic_L3_16 (solved pops=31 evals=79 maxopen=49) +[OK ] extrinsic_L3_17 (solved pops=51 evals=283 maxopen=214) +[OK ] extrinsic_L3_18 (solved pops=79 evals=531 maxopen=432) +[OK ] extrinsic_L3_7 (solved pops=632 evals=3148 maxopen=2517) +[ ] extrinsic_L2_13 (budget pops=4000 evals=20658 maxopen=16659) +[OK ] extrinsic_L3_8 (solved pops=3786 evals=26637 maxopen=22852) +[ ] extrinsic_L3_9 (budget pops=4000 evals=22261 maxopen=18262) +[ ] extrinsic_L3_10 (budget pops=4000 evals=21647 maxopen=17648) +[OK ] extrinsic_L3_23 (solved pops=56 evals=238 maxopen=183) +[ ] extrinsic_L3_19 (budget pops=4000 evals=19181 maxopen=15182) +[ ] extrinsic_L3_20 (budget pops=4000 evals=19263 maxopen=15264) +[OK ] extrinsic_L3_25 (solved pops=873 evals=5970 maxopen=5078) +[ ] extrinsic_L3_24 (budget pops=4000 evals=23172 maxopen=19173) +[ ] extrinsic_L3_21 (budget pops=4000 evals=19973 maxopen=15974) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19190 maxopen=15191) +[ ] extrinsic_L3_27 (budget pops=4000 evals=28534 maxopen=24535) +[ ] extrinsic_L3_26 (budget pops=4000 evals=29048 maxopen=25049) +[ ] extrinsic_L3_28 (budget pops=4000 evals=28953 maxopen=24954) +[ ] extrinsic_L4_1 (budget pops=4000 evals=23364 maxopen=19365) +[OK ] extrinsic_L4_3 (solved pops=1766 evals=11066 maxopen=9301) +[OK ] extrinsic_L4_2 (solved pops=3616 evals=29369 maxopen=25734) + +thread '' (89474) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L4_4 (budget pops=4000 evals=29709 maxopen=25710) +[ ] extrinsic_L4_5 (budget pops=4000 evals=31912 maxopen=27913) +[ ] extrinsic_L4_6 (budget pops=4000 evals=29299 maxopen=25300) +[ ] extrinsic_L3_29 (budget pops=4000 evals=28117 maxopen=24117) +[OK ] extrinsic_L4_12 (solved pops=453 evals=2414 maxopen=1959) +[ ] extrinsic_L4_7 (budget pops=4000 evals=28408 maxopen=24409) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26209 maxopen=22210) +[ ] extrinsic_L4_9 (budget pops=4000 evals=27715 maxopen=23716) +[ ] extrinsic_L4_10 (budget pops=4000 evals=28872 maxopen=24873) +[ ] extrinsic_L4_13 (budget pops=4000 evals=28601 maxopen=24602) +[ ] extrinsic_L4_11 (budget pops=4000 evals=34000 maxopen=30001) +[ ] extrinsic_L4_14 (budget pops=4000 evals=28552 maxopen=24553) +[ ] extrinsic_L5_1 (budget pops=4000 evals=19561 maxopen=15562) +[ ] extrinsic_L5_2 (budget pops=4000 evals=19960 maxopen=15961) +[ ] extrinsic_L5_3 (budget pops=4000 evals=20050 maxopen=16051) +[ ] extrinsic_L5_6 (budget pops=4000 evals=28540 maxopen=24541) +[ ] extrinsic_L5_5 (budget pops=4000 evals=32604 maxopen=28605) +[ ] extrinsic_L5_4 (budget pops=4000 evals=19792 maxopen=15793) +[OK ] extrinsic_L6_1 (solved pops=17 evals=43 maxopen=27) + +thread '' (89473) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L5_7 (budget pops=4000 evals=27022 maxopen=23022) +[ ] extrinsic_L5_8 (budget pops=4000 evals=25526 maxopen=21527) +[ ] extrinsic_L5_11 (budget pops=4000 evals=55257 maxopen=51258) +[ ] extrinsic_L5_9 (budget pops=4000 evals=20128 maxopen=16129) +[OK ] extrinsic_L6_6 (solved pops=467 evals=2330 maxopen=1864) +[ ] extrinsic_L5_10 (budget pops=4000 evals=22358 maxopen=18359) +[ ] extrinsic_L6_2 (budget pops=4000 evals=21310 maxopen=17311) +[OK ] extrinsic_L6_7 (solved pops=3841 evals=21017 maxopen=17177) +[ ] extrinsic_L6_4 (budget pops=4000 evals=29738 maxopen=25739) +[ ] extrinsic_L6_3 (budget pops=4000 evals=21621 maxopen=17622) +[ ] extrinsic_L6_5 (budget pops=4000 evals=20282 maxopen=16283) +[ ] extrinsic_L6_9 (budget pops=4000 evals=28758 maxopen=24759) +[ ] extrinsic_L6_8 (budget pops=4000 evals=26992 maxopen=22993) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 54/94 in 2209.3s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..6fa4438f7af161de87dcf23dd321da80b63ef214 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,887 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_8 (traces=1 evals=30) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_9 (traces=1 evals=127) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] g extrinsic_L1_2 (traces=1 evals=19) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L1_3 (traces=1 evals=19) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L1_1 (traces=1 evals=166) +[OK ] g extrinsic_L2_6 (traces=1 evals=25) +[OK ] g extrinsic_L2_5 (traces=1 evals=43) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_9 (traces=1 evals=26) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_12 (traces=1 evals=55) +[OK ] - extrinsic_L0_5 (traces=2 evals=372) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L3_4 (traces=2 evals=511) +[OK ] - extrinsic_L3_5 (traces=2 evals=535) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) + +thread '' (870458) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L2_13 (traces=16 evals=9633) +[ ] - extrinsic_L3_7 (traces=17 evals=8260) +[ ] - extrinsic_L3_1 (traces=17 evals=19510) +[ ] - extrinsic_L2_2 (traces=17 evals=21572) +[OK ] - extrinsic_L3_11 (traces=3 evals=647) +[ ] - extrinsic_L0_12 (traces=17 evals=18311) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[OK ] g extrinsic_L3_14 (traces=1 evals=150) +[OK ] - extrinsic_L3_9 (traces=8 evals=9081) +[ ] - extrinsic_L3_10 (traces=17 evals=10090) +[OK ] - extrinsic_L3_12 (traces=8 evals=4784) +[OK ] - extrinsic_L3_18 (traces=2 evals=542) +[OK ] - extrinsic_L3_2 (traces=10 evals=10465) + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L3_15 (traces=12 evals=15205) +[ ] - extrinsic_L3_19 (traces=17 evals=6028) + +thread '' (870456) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870456) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_8 (traces=17 evals=29156) +[OK ] - extrinsic_L3_16 (traces=15 evals=13504) + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L3_23 (traces=10 evals=3255) +[OK ] - extrinsic_L3_17 (traces=8 evals=14856) +[ ] - extrinsic_L3_21 (traces=17 evals=8865) + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_22 (traces=17 evals=13575) +[ ] - extrinsic_L3_20 (traces=17 evals=10291) +[ ] - extrinsic_L3_24 (traces=17 evals=7196) + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_1 (traces=17 evals=14470) + +thread '' (870456) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_28 (traces=17 evals=17353) +[ ] - extrinsic_L3_25 (traces=17 evals=10150) + +thread '' (870458) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870458) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_27 (traces=17 evals=22204) +[ ] - extrinsic_L3_26 (traces=15 evals=20204) +[ ] - extrinsic_L3_29 (traces=5 evals=32154) +[ ] - extrinsic_L4_2 (traces=15 evals=22949) +[ ] - extrinsic_L4_3 (traces=17 evals=31351) +[ ] - extrinsic_L4_4 (traces=7 evals=16741) +[ ] - extrinsic_L4_6 (traces=17 evals=24130) +[ ] - extrinsic_L4_5 (traces=7 evals=15729) +[ ] - extrinsic_L4_8 (traces=17 evals=18765) +[ ] - extrinsic_L4_7 (traces=17 evals=12104) +[ ] - extrinsic_L4_9 (traces=17 evals=20712) + +thread '' (870459) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870459) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870459) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870459) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_10 (traces=17 evals=18550) + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_11 (traces=17 evals=24692) +[ ] - extrinsic_L4_13 (traces=17 evals=25278) +[ ] - extrinsic_L5_2 (traces=17 evals=7359) +[ ] - extrinsic_L5_1 (traces=17 evals=19033) +[ ] - extrinsic_L4_14 (traces=17 evals=33333) +[ ] - extrinsic_L4_12 (traces=17 evals=24562) + +thread '' (870459) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_5 (traces=17 evals=20363) + +thread '' (870457) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870457) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870457) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_7 (traces=17 evals=22109) + +thread '' (870457) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870457) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=17 evals=14724) +[ ] - extrinsic_L5_3 (traces=17 evals=28778) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) +[ ] - extrinsic_L5_9 (traces=17 evals=8838) +[ ] - extrinsic_L5_4 (traces=3 evals=32747) + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_6 (traces=14 evals=36579) + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870455) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_10 (traces=17 evals=13059) +[OK ] g extrinsic_L6_6 (traces=1 evals=56) + +thread '' (870452) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_7 (traces=17 evals=6584) +[ ] - extrinsic_L6_3 (traces=17 evals=20530) +[ ] - extrinsic_L5_11 (traces=15 evals=23457) +[ ] - extrinsic_L6_2 (traces=4 evals=22894) + +thread '' (870456) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_4 (traces=11 evals=76847) +[ ] - extrinsic_L6_5 (traces=14 evals=64802) +[ ] - extrinsic_L6_9 (traces=15 evals=20784) +[ ] - extrinsic_L6_8 (traces=5 evals=117561) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 46/94 in 3989.0s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..8ceac5ae3638cd9cec940f240e0028828be0d3d9 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 60 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s44/train.log b/experiments/learnability/train_policy_only/minimo_1pt/s44/train.log new file mode 100644 index 0000000000000000000000000000000000000000..29dc3e52a1b62921099fc62a3410bf26024e06c0 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s44/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_053054-z2j5ja9t +[2026-06-28T05:30:50.843892] Seeded RNGs with seed=44 +[2026-06-28T05:30:50.844156] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-28T05:30:54.256499] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json + 1880 training examples loaded. + +============================================================ +[2026-06-28T05:30:54.258896] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1880 -> 1880 unique examples + Epoch 1/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 60 total steps, 1880 unique examples (batch_size=64) +[2026-06-28T05:31:07.163891] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:31:07.171972] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s44/2026-06-28_05-30-50/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 60} diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/summary.json b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..cd281b6ecb9edda1f6bfcb54b15e803e1eb9b1f8 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_1_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 60 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/ablation_config.json b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/ablation_config.json new file mode 100644 index 0000000000000000000000000000000000000000..ef9839e91529f242f0fa0d586a563f31e425e03e --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/ablation_config.json @@ -0,0 +1,8 @@ +{ + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1, + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json" +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..c223916a94f044d2d14068f458b07ecba6927573 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,779 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_8 (solved pops=10 evals=29 maxopen=20) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_7 (solved pops=15 evals=42 maxopen=28) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L0_14 (solved pops=10 evals=31 maxopen=22) +[OK ] extrinsic_L1_2 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L1_3 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L2_1 (solved pops=17 evals=43 maxopen=27) +[OK ] extrinsic_L2_4 (solved pops=15 evals=60 maxopen=46) +[OK ] extrinsic_L2_3 (solved pops=15 evals=60 maxopen=46) +[OK ] extrinsic_L2_6 (solved pops=15 evals=33 maxopen=19) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_8 (solved pops=11 evals=30 maxopen=20) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L2_9 (solved pops=14 evals=50 maxopen=37) +[OK ] extrinsic_L3_1 (solved pops=13 evals=53 maxopen=41) +[OK ] extrinsic_L0_12 (solved pops=75 evals=446 maxopen=355) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L3_4 (solved pops=14 evals=77 maxopen=43) +[OK ] extrinsic_L2_5 (solved pops=72 evals=239 maxopen=168) +[OK ] extrinsic_L2_12 (solved pops=49 evals=145 maxopen=97) +[OK ] extrinsic_L3_2 (solved pops=33 evals=115 maxopen=83) +[OK ] extrinsic_L3_5 (solved pops=14 evals=76 maxopen=42) +[OK ] extrinsic_L3_6 (solved pops=60 evals=203 maxopen=144) +[OK ] extrinsic_L2_2 (solved pops=146 evals=584 maxopen=439) +[OK ] extrinsic_L3_11 (solved pops=58 evals=239 maxopen=179) +[OK ] extrinsic_L3_12 (solved pops=72 evals=313 maxopen=222) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=11 evals=45 maxopen=35) +[OK ] extrinsic_L3_15 (solved pops=72 evals=315 maxopen=244) +[OK ] extrinsic_L3_16 (solved pops=31 evals=92 maxopen=62) +[OK ] extrinsic_L3_17 (solved pops=38 evals=206 maxopen=150) +[OK ] extrinsic_L3_18 (solved pops=46 evals=307 maxopen=241) +[OK ] extrinsic_L3_7 (solved pops=684 evals=3363 maxopen=2680) +[OK ] extrinsic_L3_8 (solved pops=1484 evals=10535 maxopen=9052) +[OK ] extrinsic_L3_10 (solved pops=1700 evals=8996 maxopen=7274) +[OK ] extrinsic_L3_9 (solved pops=2021 evals=10865 maxopen=8822) +[OK ] extrinsic_L3_23 (solved pops=44 evals=184 maxopen=141) +[ ] extrinsic_L2_13 (budget pops=4000 evals=19352 maxopen=15353) +[OK ] extrinsic_L3_25 (solved pops=962 evals=6093 maxopen=5132) +[ ] extrinsic_L3_19 (budget pops=4000 evals=18982 maxopen=14983) +[ ] extrinsic_L3_20 (budget pops=4000 evals=19689 maxopen=15690) +[ ] extrinsic_L3_24 (budget pops=4000 evals=22439 maxopen=18440) +[ ] extrinsic_L3_21 (budget pops=4000 evals=20020 maxopen=16021) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19496 maxopen=15497) +[ ] extrinsic_L4_1 (budget pops=4000 evals=23412 maxopen=19413) + +thread '' (16389) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L3_26 (budget pops=4000 evals=27993 maxopen=23994) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26852 maxopen=22853) +[ ] extrinsic_L4_2 (budget pops=4000 evals=29560 maxopen=25561) +[OK ] extrinsic_L4_3 (solved pops=1535 evals=8346 maxopen=6812) +[ ] extrinsic_L3_28 (budget pops=4000 evals=28743 maxopen=24744) + +thread '' (16389) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L3_29 (budget pops=4000 evals=26850 maxopen=22849) +[ ] extrinsic_L4_4 (budget pops=4000 evals=29158 maxopen=25159) +[ ] extrinsic_L4_5 (budget pops=4000 evals=31738 maxopen=27739) +[ ] extrinsic_L4_6 (budget pops=4000 evals=29191 maxopen=25192) +[ ] extrinsic_L4_7 (budget pops=4000 evals=25892 maxopen=21893) +[OK ] extrinsic_L4_12 (solved pops=478 evals=2426 maxopen=1946) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25527 maxopen=21528) +[ ] extrinsic_L4_10 (budget pops=4000 evals=27496 maxopen=23497) +[ ] extrinsic_L4_9 (budget pops=4000 evals=27505 maxopen=23506) +[ ] extrinsic_L4_11 (budget pops=4000 evals=30422 maxopen=26423) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26674 maxopen=22675) +[ ] extrinsic_L4_14 (budget pops=4000 evals=28653 maxopen=24654) +[ ] extrinsic_L5_1 (budget pops=4000 evals=19687 maxopen=15688) +[ ] extrinsic_L5_3 (budget pops=4000 evals=20107 maxopen=16108) + +thread '' (16388) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L5_2 (budget pops=4000 evals=19370 maxopen=15371) + +thread '' (16388) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (16391) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] extrinsic_L5_6 (budget pops=4000 evals=26742 maxopen=22743) + +thread '' (16388) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_5 (budget pops=4000 evals=33454 maxopen=29452) +[ ] extrinsic_L5_4 (budget pops=4000 evals=19561 maxopen=15562) +[OK ] extrinsic_L6_1 (solved pops=23 evals=57 maxopen=35) + +thread '' (16391) panicked at src/universe/term.rs:851:75: +mid > len +[ ] extrinsic_L5_7 (budget pops=4000 evals=25712 maxopen=21711) +[ ] extrinsic_L5_8 (budget pops=4000 evals=25914 maxopen=21915) +[ ] extrinsic_L5_9 (budget pops=4000 evals=20274 maxopen=16275) +[ ] extrinsic_L5_11 (budget pops=4000 evals=55364 maxopen=51365) +[OK ] extrinsic_L6_6 (solved pops=733 evals=3715 maxopen=2983) +[ ] extrinsic_L5_10 (budget pops=4000 evals=21834 maxopen=17835) +[ ] extrinsic_L6_2 (budget pops=4000 evals=23332 maxopen=19333) +[ ] extrinsic_L6_4 (budget pops=4000 evals=29423 maxopen=25424) +[ ] extrinsic_L6_3 (budget pops=4000 evals=23969 maxopen=19970) +[ ] extrinsic_L6_7 (budget pops=4000 evals=21761 maxopen=17762) +[ ] extrinsic_L6_5 (budget pops=4000 evals=21327 maxopen=17328) +[ ] extrinsic_L6_9 (budget pops=4000 evals=27137 maxopen=23138) +[ ] extrinsic_L6_8 (budget pops=4000 evals=27215 maxopen=23216) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 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-> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]])].", + "a or_il", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or x (not x)))]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]).", + "c em", + "=> (em goal0).", + "a x3", + "=> (or (not false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not false) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : 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[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x5", + "=> (x5 x4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em x1).", + "a x4", + "=> (iff (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> .", + "intro.", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])." + ] + }, + { + "mode": "sample", 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[[x0 -> x1] -> (not x1)].", + "a or_e", + "=> [x -> [x -> (not x1)]]; [[x0 -> x1] -> [x -> (not x1)]].", + "a or_e", + "=> [x -> [x -> [x -> (not x1)]]]; [[x0 -> x1] -> [x -> [x -> (not x1)]]].", + "intro.", + "intro.", + "a x4", + "=> (and [x -> (not x1)] x0).", + "a or_e", + "=> [x -> (and [x -> (not x1)] x0)]; [[x0 -> x1] -> (and [x -> (not x1)] x0)].", + "a or_e", + "=> [x -> [x -> (and [x -> (not x1)] x0)]]; [[x0 -> x1] -> [x -> (and [x -> (not x1)] x0)]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [x -> false]); [x -> false].", + "a not_i", + "=> [[x -> false] -> false].", + "a x4", + "=> (and [[x -> false] -> false] [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..a5c187d3dd78adc7627c39fb7ea6a695ab06781f --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,929 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_8 (traces=1 evals=25) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] g extrinsic_L1_2 (traces=1 evals=19) +[OK ] g extrinsic_L1_3 (traces=1 evals=19) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] - extrinsic_L0_5 (traces=2 evals=372) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_5 (traces=1 evals=48) +[OK ] g extrinsic_L2_6 (traces=1 evals=25) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_9 (traces=1 evals=26) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] - extrinsic_L0_9 (traces=2 evals=427) +[OK ] g extrinsic_L2_12 (traces=1 evals=50) +[OK ] g extrinsic_L2_13 (traces=1 evals=96) +[OK ] - extrinsic_L1_1 (traces=2 evals=403) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L3_4 (traces=2 evals=564) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L3_5 (traces=2 evals=1140) + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871235) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871235) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_2 (traces=17 evals=9851) +[OK ] - extrinsic_L3_2 (traces=13 evals=6503) +[OK ] - extrinsic_L3_1 (traces=8 evals=13416) +[OK ] - extrinsic_L3_11 (traces=3 evals=693) +[OK ] - extrinsic_L3_12 (traces=8 evals=2669) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[OK ] - extrinsic_L3_9 (traces=11 evals=7152) +[OK ] - extrinsic_L3_14 (traces=4 evals=1340) + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_8 (traces=17 evals=17671) +[OK ] - extrinsic_L3_17 (traces=3 evals=1127) +[OK ] - extrinsic_L3_15 (traces=10 evals=3262) +[OK ] - extrinsic_L3_18 (traces=2 evals=542) +[ ] - extrinsic_L3_10 (traces=17 evals=13099) +[OK ] - extrinsic_L3_16 (traces=10 evals=8596) + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_21 (traces=17 evals=7080) +[OK ] g extrinsic_L3_23 (traces=1 evals=114) + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=17 evals=15505) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_22 (traces=17 evals=12274) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=17 evals=20007) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_12 (traces=7 evals=14931) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_20 (traces=17 evals=13441) + +thread '' (871235) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_24 (traces=17 evals=16061) +[ ] - extrinsic_L3_27 (traces=17 evals=14072) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_1 (traces=17 evals=9073) + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_2 (traces=17 evals=17877) + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_26 (traces=17 evals=15443) +[ ] - extrinsic_L3_28 (traces=17 evals=26085) +[ ] - extrinsic_L3_25 (traces=7 evals=13777) + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_4 (traces=17 evals=18588) +[ ] - extrinsic_L3_29 (traces=14 evals=34985) +[ ] - extrinsic_L4_3 (traces=17 evals=31597) + +thread '' (871238) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L4_7 (traces=17 evals=17438) +[ ] - extrinsic_L4_6 (traces=17 evals=17007) +[ ] - extrinsic_L4_9 (traces=17 evals=20263) +[ ] - extrinsic_L4_8 (traces=17 evals=22675) +[ ] - extrinsic_L4_10 (traces=17 evals=24976) +[ ] - extrinsic_L4_5 (traces=7 evals=13778) +[ ] - extrinsic_L4_13 (traces=17 evals=7796) +[ ] - extrinsic_L4_11 (traces=17 evals=27955) +[OK ] - extrinsic_L5_2 (traces=12 evals=3777) +[ ] - extrinsic_L5_1 (traces=17 evals=6204) + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_12 (traces=17 evals=29780) +[ ] - extrinsic_L5_3 (traces=17 evals=7354) + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871234) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_5 (traces=17 evals=7733) + +thread '' (871231) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (871231) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871237) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=17 evals=8042) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_14 (traces=17 evals=32744) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_7 (traces=17 evals=12961) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (871236) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_6 (traces=17 evals=19827) + +thread '' (871238) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=17 evals=13783) +[ ] - extrinsic_L5_9 (traces=17 evals=18367) +[ ] - extrinsic_L6_3 (traces=17 evals=7915) +[OK ] g extrinsic_L6_6 (traces=1 evals=56) +[ ] - extrinsic_L6_5 (traces=17 evals=7130) +[ ] - extrinsic_L5_11 (traces=13 evals=24550) +[ ] - extrinsic_L5_10 (traces=4 evals=21784) +[ ] - extrinsic_L6_2 (traces=15 evals=20039) +[ ] - extrinsic_L6_7 (traces=17 evals=23042) +[ ] - extrinsic_L6_4 (traces=5 evals=61100) +[ ] - extrinsic_L6_8 (traces=5 evals=117427) +[ ] - extrinsic_L6_9 (traces=17 evals=22820) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 48/94 in 3360.9s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..8ceac5ae3638cd9cec940f240e0028828be0d3d9 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 60 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s45/train.log b/experiments/learnability/train_policy_only/minimo_1pt/s45/train.log new file mode 100644 index 0000000000000000000000000000000000000000..796197ff05ea40534e2f22d2e38c7c1ff5a8abde --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s45/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_053114-vxojf5d0 +[2026-06-28T05:31:10.329429] Seeded RNGs with seed=45 +[2026-06-28T05:31:10.329716] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-28T05:31:13.819302] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json + 1880 training examples loaded. + +============================================================ +[2026-06-28T05:31:13.821924] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1880 -> 1880 unique examples + Epoch 1/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/30 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 60 total steps, 1880 unique examples (batch_size=64) +[2026-06-28T05:31:26.766008] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:31:26.774302] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s45/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 60}