diff --git a/experiments/learnability/bestfirst_eval/eval_driver.log b/experiments/learnability/bestfirst_eval/eval_driver.log new file mode 100644 index 0000000000000000000000000000000000000000..8c30b0a65b65ecdfca2740de69b261cdceb702e3 --- /dev/null +++ b/experiments/learnability/bestfirst_eval/eval_driver.log @@ -0,0 +1,77 @@ +[2026-06-29 03:08:47] ===== START: 22 best-first evals (max_pops=4000 timeout=600s) on GPUs 0 1 2 3 ===== +[2026-06-29 03:08:47] EVAL [0/22] base/minimo_0pt -> gpu 0 +[2026-06-29 03:08:47] EVAL [1/22] base/minimo_1pt -> gpu 1 +[2026-06-29 03:08:47] EVAL [2/22] final/minimo_0pt/s42/2026-06-28_05-29-55 -> gpu 2 +[2026-06-29 03:08:47] EVAL [3/22] final/minimo_0pt/s43/2026-06-28_05-29-55 -> gpu 3 +[2026-06-29 03:08:54] EVAL DONE base/minimo_0pt +[2026-06-29 03:08:55] EVAL DONE base/minimo_1pt +[2026-06-29 03:10:56] EVAL DONE final/minimo_0pt/s43/2026-06-28_05-29-55 +[2026-06-29 03:10:56] EVAL DONE final/minimo_0pt/s42/2026-06-28_05-29-55 +[2026-06-29 03:11:16] ===== START: 22 best-first evals (max_pops=4000 timeout=600s) on GPUs 0 1 2 3 ===== +[2026-06-29 03:11:16] EVAL [0/22] base/minimo_0pt -> gpu 0 +[2026-06-29 03:11:16] EVAL [1/22] base/minimo_1pt -> gpu 1 +[2026-06-29 03:11:16] EVAL [2/22] final/minimo_0pt/s42/2026-06-28_05-29-55 -> gpu 2 +[2026-06-29 03:11:16] EVAL [3/22] final/minimo_0pt/s43/2026-06-28_05-29-55 -> gpu 3 +[2026-06-29 03:47:10] EVAL DONE base/minimo_1pt +[2026-06-29 03:56:56] EVAL DONE final/minimo_0pt/s42/2026-06-28_05-29-55 +[2026-06-29 03:57:08] EVAL DONE final/minimo_0pt/s43/2026-06-28_05-29-55 +[2026-06-29 03:57:33] EVAL DONE base/minimo_0pt +[2026-06-29 03:57:33] EVAL [4/22] final/minimo_0pt/s44/2026-06-28_05-30-13 -> gpu 0 +[2026-06-29 03:57:33] EVAL [5/22] final/minimo_0pt/s45/2026-06-28_05-30-13 -> gpu 1 +[2026-06-29 03:57:33] EVAL [6/22] final/minimo_0pt/s46/2026-06-28_05-30-31 -> gpu 2 +[2026-06-29 03:57:33] EVAL [7/22] final/minimo_1pt/s42/2026-06-28_05-30-31 -> gpu 3 +[2026-06-29 04:36:09] EVAL DONE final/minimo_1pt/s42/2026-06-28_05-30-31 +[2026-06-29 04:43:14] EVAL DONE final/minimo_0pt/s46/2026-06-28_05-30-31 +[2026-06-29 04:43:24] EVAL DONE final/minimo_0pt/s45/2026-06-28_05-30-13 +[2026-06-29 04:43:42] EVAL DONE final/minimo_0pt/s44/2026-06-28_05-30-13 +[2026-06-29 04:43:42] EVAL [8/22] final/minimo_1pt/s43/2026-06-28_05-30-50 -> gpu 0 +[2026-06-29 04:43:42] EVAL [9/22] final/minimo_1pt/s44/2026-06-28_05-30-50 -> gpu 1 +[2026-06-29 04:43:42] EVAL [10/22] final/minimo_1pt/s45/2026-06-28_05-31-10 -> gpu 2 +[2026-06-29 04:43:42] EVAL [11/22] final/minimo_1pt/s46/2026-06-28_05-31-10 -> gpu 3 +[2026-06-29 05:19:29] EVAL DONE final/minimo_1pt/s43/2026-06-28_05-30-50 +[2026-06-29 05:19:45] EVAL DONE final/minimo_1pt/s44/2026-06-28_05-30-50 +[2026-06-29 05:21:14] EVAL DONE final/minimo_1pt/s45/2026-06-28_05-31-10 +[2026-06-29 05:23:48] EVAL DONE final/minimo_1pt/s46/2026-06-28_05-31-10 +[2026-06-29 05:23:48] EVAL [12/22] mid/minimo_0pt/s42/2026-06-28_05-29-55 -> gpu 0 +[2026-06-29 05:23:48] EVAL [13/22] mid/minimo_0pt/s43/2026-06-28_05-29-55 -> gpu 1 +[2026-06-29 05:23:48] EVAL [14/22] mid/minimo_0pt/s44/2026-06-28_05-30-13 -> gpu 2 +[2026-06-29 05:23:48] EVAL [15/22] mid/minimo_0pt/s45/2026-06-28_05-30-13 -> gpu 3 +[2026-06-29 06:09:37] EVAL DONE mid/minimo_0pt/s44/2026-06-28_05-30-13 +[2026-06-29 06:09:43] EVAL DONE mid/minimo_0pt/s43/2026-06-28_05-29-55 +[2026-06-29 06:09:43] EVAL DONE mid/minimo_0pt/s45/2026-06-28_05-30-13 +[2026-06-29 06:10:07] EVAL DONE mid/minimo_0pt/s42/2026-06-28_05-29-55 +[2026-06-29 06:10:07] EVAL [16/22] mid/minimo_0pt/s46/2026-06-28_05-30-31 -> gpu 0 +[2026-06-29 06:10:07] EVAL [17/22] mid/minimo_1pt/s42/2026-06-28_05-30-31 -> gpu 1 +[2026-06-29 06:10:07] EVAL [18/22] mid/minimo_1pt/s43/2026-06-28_05-30-50 -> gpu 2 +[2026-06-29 06:10:07] EVAL [19/22] mid/minimo_1pt/s44/2026-06-28_05-30-50 -> gpu 3 +[2026-06-29 06:47:00] EVAL DONE mid/minimo_1pt/s44/2026-06-28_05-30-50 +[2026-06-29 06:49:32] EVAL DONE mid/minimo_1pt/s42/2026-06-28_05-30-31 +[2026-06-29 06:50:23] EVAL DONE mid/minimo_1pt/s43/2026-06-28_05-30-50 +[2026-06-29 06:56:14] EVAL DONE mid/minimo_0pt/s46/2026-06-28_05-30-31 +[2026-06-29 06:56:14] EVAL [20/22] mid/minimo_1pt/s45/2026-06-28_05-31-10 -> gpu 0 +[2026-06-29 06:56:14] EVAL [21/22] mid/minimo_1pt/s46/2026-06-28_05-31-10 -> gpu 1 +[2026-06-29 07:31:27] EVAL DONE mid/minimo_1pt/s46/2026-06-28_05-31-10 +[2026-06-29 07:31:44] EVAL DONE mid/minimo_1pt/s45/2026-06-28_05-31-10 +[2026-06-29 07:31:44] --- All evals complete --- +26 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/bestfirst_eval/minimo_0pt_base_bf_extrinsic-95.json +50 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/bestfirst_eval/minimo_1pt_base_bf_extrinsic-95.json +27 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json +27 / 94 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4000, + "evals_used": 30994, + "max_open": 26995, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/bestfirst_eval/minimo_0pt_base_bf_extrinsic-95.log b/experiments/learnability/bestfirst_eval/minimo_0pt_base_bf_extrinsic-95.log new file mode 100644 index 0000000000000000000000000000000000000000..ac1f111f27c7024b4ea77177ce3fb3fa40afc1be --- /dev/null +++ b/experiments/learnability/bestfirst_eval/minimo_0pt_base_bf_extrinsic-95.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_6 (solved pops=53 evals=346 maxopen=294) +[OK ] extrinsic_L0_2 (solved pops=55 evals=350 maxopen=296) +[OK ] extrinsic_L0_5 (solved pops=57 evals=353 maxopen=297) +[OK ] extrinsic_L0_3 (solved pops=64 evals=395 maxopen=332) +[OK ] extrinsic_L0_10 (solved pops=11 evals=75 maxopen=65) +[OK ] extrinsic_L0_7 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_8 (solved pops=53 evals=347 maxopen=295) +[OK ] extrinsic_L0_13 (solved pops=25 evals=176 maxopen=152) +[OK ] extrinsic_L0_9 (solved pops=53 evals=362 maxopen=294) +[OK ] extrinsic_L0_4 (solved pops=201 evals=1060 maxopen=860) +[OK ] extrinsic_L1_4 (solved pops=18 evals=121 maxopen=102) +[OK ] extrinsic_L0_11 (solved pops=210 evals=1157 maxopen=948) +[OK ] extrinsic_L1_1 (solved pops=225 evals=1196 maxopen=954) +[OK ] extrinsic_L1_2 (solved pops=452 evals=2444 maxopen=1993) +[OK ] extrinsic_L1_3 (solved pops=452 evals=2441 maxopen=1990) +[OK ] extrinsic_L2_1 (solved pops=1414 evals=7998 maxopen=6585) +[OK ] extrinsic_L2_6 (solved pops=1418 evals=8021 maxopen=6604) +[OK ] extrinsic_L2_7 (solved pops=898 evals=4947 maxopen=4050) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26022 maxopen=22023) +[ ] extrinsic_L0_14 (budget pops=4000 evals=26308 maxopen=22309) +[ ] extrinsic_L2_3 (budget pops=4000 evals=26017 maxopen=22018) +[OK ] extrinsic_L2_11 (solved pops=22 evals=145 maxopen=122) +[ ] extrinsic_L2_4 (budget pops=4000 evals=26012 maxopen=22013) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25845 maxopen=21846) +[OK ] extrinsic_L2_9 (solved pops=995 evals=5535 maxopen=4541) +[OK ] extrinsic_L2_12 (solved pops=1322 evals=7487 maxopen=6166) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26325 maxopen=22326) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26099 maxopen=22100) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25708 maxopen=21709) +[ ] extrinsic_L3_1 (budget pops=4000 evals=26029 maxopen=22030) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25731 maxopen=21732) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25729 maxopen=21730) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25927 maxopen=21928) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25932 maxopen=21933) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25833 maxopen=21834) +[ ] extrinsic_L3_7 (budget pops=4000 evals=26004 maxopen=22005) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26146 maxopen=22147) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26098 maxopen=22099) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26006 maxopen=22007) +[OK ] extrinsic_L3_13 (solved pops=3008 evals=17936 maxopen=14929) +[OK ] extrinsic_L3_14 (solved pops=3163 evals=19748 maxopen=16586) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25697 maxopen=21698) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25704 maxopen=21705) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26079 maxopen=22080) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26053 maxopen=22054) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25822 maxopen=21823) +[ ] extrinsic_L3_18 (budget pops=4000 evals=26002 maxopen=22003) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25892 maxopen=21893) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26009 maxopen=22010) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25965 maxopen=21966) +[ ] extrinsic_L3_22 (budget pops=4000 evals=26014 maxopen=22015) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26021 maxopen=22022) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26314 maxopen=22315) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26023 maxopen=22024) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27014 maxopen=23015) +[ ] extrinsic_L3_27 (budget pops=4000 evals=25989 maxopen=21990) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25958 maxopen=21959) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26683 maxopen=22684) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26769 maxopen=22770) +[ ] extrinsic_L4_2 (budget pops=4000 evals=25941 maxopen=21942) +[ ] extrinsic_L4_3 (budget pops=4000 evals=25895 maxopen=21896) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25861 maxopen=21862) +[ ] extrinsic_L4_5 (budget pops=4000 evals=25952 maxopen=21953) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25879 maxopen=21880) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26271 maxopen=22272) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25910 maxopen=21911) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26151 maxopen=22152) +[OK ] extrinsic_L4_12 (solved pops=1261 evals=7127 maxopen=5864) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25478 maxopen=21479) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26382 maxopen=22383) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25817 maxopen=21818) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26299 maxopen=22300) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26391 maxopen=22392) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26218 maxopen=22219) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26210 maxopen=22211) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26331 maxopen=22332) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26028 maxopen=22029) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26112 maxopen=22113) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26387 maxopen=22388) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26480 maxopen=22481) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26331 maxopen=22332) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26648 maxopen=22649) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26031 maxopen=22032) +[ ] extrinsic_L5_11 (budget pops=4000 evals=30991 maxopen=26992) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30992 maxopen=26993) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31039 maxopen=27040) +[ ] extrinsic_L6_3 (budget pops=4000 evals=30994 maxopen=26995) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31015 maxopen=27016) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25918 maxopen=21919) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25846 maxopen=21847) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31196 maxopen=27197) +[ ] extrinsic_L6_9 (budget pops=4000 evals=30994 maxopen=26995) +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 -> 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'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/bestfirst_eval/minimo_0pt_base_bf_extrinsic-95.json +Solved 26/94 in 2773.7s diff --git a/experiments/learnability/bestfirst_eval/minimo_1pt_base_bf_extrinsic-95.json b/experiments/learnability/bestfirst_eval/minimo_1pt_base_bf_extrinsic-95.json new file mode 100644 index 0000000000000000000000000000000000000000..ac439c41facfc2270634f72803be34ebc329c135 --- /dev/null +++ b/experiments/learnability/bestfirst_eval/minimo_1pt_base_bf_extrinsic-95.json @@ -0,0 +1,1344 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/checkpoints/dnn3_bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "problemset": "extrinsic-95", + "max_pops": 4000, + "max_actions": 0, + "timeout": 600.0, + "workers": 6, + "num_problems": 94, + "num_solved": 50, + "elapsed_sec": 2150.6519980430603, + "results": [ + { + "solved": true, + "outcome": "solved", + "pops_used": 2, + "evals_used": 6, + "max_open": 3, + "solution_actions": [ + "intro.", + "intro." + ], + "problem": "extrinsic_L0_1" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 14, + "evals_used": 76, + "max_open": 63, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "c and_el", + "=> 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20501, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/bestfirst_eval/minimo_1pt_base_bf_extrinsic-95.log b/experiments/learnability/bestfirst_eval/minimo_1pt_base_bf_extrinsic-95.log new file mode 100644 index 0000000000000000000000000000000000000000..ef0dc6e2900d7bde44c33594bb096a41c6abf218 --- /dev/null +++ b/experiments/learnability/bestfirst_eval/minimo_1pt_base_bf_extrinsic-95.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_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_5 (solved pops=9 evals=48 maxopen=40) +[OK ] extrinsic_L0_4 (solved pops=11 evals=68 maxopen=58) +[OK ] extrinsic_L0_2 (solved pops=14 evals=76 maxopen=63) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_8 (solved pops=13 evals=75 maxopen=63) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_9 (solved pops=11 evals=69 maxopen=43) +[OK ] extrinsic_L0_7 (solved pops=17 evals=84 maxopen=68) +[OK ] extrinsic_L0_11 (solved pops=15 evals=76 maxopen=62) +[OK ] extrinsic_L0_12 (solved pops=14 evals=59 maxopen=29) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_1 (solved pops=16 evals=97 maxopen=64) +[OK ] extrinsic_L1_2 (solved pops=26 evals=198 maxopen=154) +[OK ] extrinsic_L1_3 (solved pops=25 evals=182 maxopen=139) +[OK ] extrinsic_L0_14 (solved pops=44 evals=285 maxopen=242) +[OK ] extrinsic_L2_1 (solved pops=66 evals=351 maxopen=286) +[OK ] extrinsic_L2_7 (solved pops=32 evals=192 maxopen=161) +[OK ] extrinsic_L2_4 (solved pops=86 evals=567 maxopen=482) +[OK ] extrinsic_L2_3 (solved pops=104 evals=679 maxopen=576) +[OK ] extrinsic_L2_9 (solved pops=47 evals=356 maxopen=310) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_10 (solved pops=46 evals=313 maxopen=268) +[OK ] extrinsic_L2_6 (solved pops=148 evals=852 maxopen=705) +[OK ] extrinsic_L2_8 (solved pops=100 evals=597 maxopen=498) +[OK ] extrinsic_L3_1 (solved pops=61 evals=445 maxopen=385) +[OK ] extrinsic_L2_12 (solved pops=109 evals=652 maxopen=544) +[OK ] extrinsic_L3_3 (solved pops=40 evals=266 maxopen=227) +[OK ] extrinsic_L3_4 (solved pops=82 evals=587 maxopen=485) +[OK ] extrinsic_L3_5 (solved pops=83 evals=618 maxopen=515) +[OK ] extrinsic_L2_2 (solved pops=410 evals=2108 maxopen=1699) +[OK ] extrinsic_L3_2 (solved pops=473 evals=2519 maxopen=2047) +[OK ] extrinsic_L2_5 (solved pops=795 evals=4382 maxopen=3588) +[OK ] extrinsic_L3_6 (solved pops=740 evals=4100 maxopen=3361) +[OK ] extrinsic_L3_11 (solved pops=252 evals=1326 maxopen=1072) +[OK ] extrinsic_L3_12 (solved pops=217 evals=1157 maxopen=941) +[OK ] extrinsic_L3_13 (solved pops=30 evals=185 maxopen=156) +[OK ] extrinsic_L3_14 (solved pops=46 evals=338 maxopen=293) +[OK ] extrinsic_L3_15 (solved pops=1663 evals=9917 maxopen=8255) +[OK ] extrinsic_L3_16 (solved pops=181 evals=979 maxopen=799) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25210 maxopen=21211) +[ ] extrinsic_L3_7 (budget pops=4000 evals=24794 maxopen=20795) +[OK ] extrinsic_L3_18 (solved pops=592 evals=3428 maxopen=2816) +[OK ] extrinsic_L3_17 (solved pops=1359 evals=8178 maxopen=6801) +[ ] extrinsic_L3_8 (budget pops=4000 evals=28200 maxopen=24201) +[ ] extrinsic_L3_9 (budget pops=4000 evals=25416 maxopen=21417) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26882 maxopen=22883) +[OK ] extrinsic_L3_23 (solved pops=477 evals=2990 maxopen=2514) +[OK ] extrinsic_L3_25 (solved pops=495 evals=2874 maxopen=2360) +[ ] extrinsic_L3_19 (budget pops=4000 evals=23887 maxopen=19888) +[ ] extrinsic_L3_24 (budget pops=4000 evals=27030 maxopen=23031) +[ ] extrinsic_L3_20 (budget pops=4000 evals=25074 maxopen=21075) +[ ] extrinsic_L3_21 (budget pops=4000 evals=24618 maxopen=20619) +[ ] extrinsic_L3_22 (budget pops=4000 evals=24240 maxopen=20241) +[ ] extrinsic_L3_26 (budget pops=4000 evals=28211 maxopen=24212) +[OK ] extrinsic_L4_3 (solved pops=989 evals=5608 maxopen=4620) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26839 maxopen=22840) +[OK ] extrinsic_L4_2 (solved pops=3886 evals=32218 maxopen=28333) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26923 maxopen=22924) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26199 maxopen=22200) +[ ] extrinsic_L4_4 (budget pops=4000 evals=28098 maxopen=24099) +[ ] extrinsic_L3_29 (budget pops=4000 evals=33376 maxopen=29377) +[ ] extrinsic_L4_5 (budget pops=4000 evals=29691 maxopen=25692) +[ ] extrinsic_L4_6 (budget pops=4000 evals=28385 maxopen=24386) +[OK ] extrinsic_L4_12 (solved pops=139 evals=808 maxopen=667) +[ ] extrinsic_L4_7 (budget pops=4000 evals=24224 maxopen=20225) +[ ] extrinsic_L4_8 (budget pops=4000 evals=27966 maxopen=23967) +[ ] extrinsic_L4_9 (budget pops=4000 evals=24187 maxopen=20188) +[ ] extrinsic_L4_10 (budget pops=4000 evals=28454 maxopen=24455) +[ ] extrinsic_L4_13 (budget pops=4000 evals=27712 maxopen=23713) +[ ] extrinsic_L4_11 (budget pops=4000 evals=32557 maxopen=28558) +[ ] extrinsic_L4_14 (budget pops=4000 evals=27657 maxopen=23658) +[ ] extrinsic_L5_1 (budget pops=4000 evals=30373 maxopen=26374) +[ ] extrinsic_L5_2 (budget pops=4000 evals=29841 maxopen=25842) +[ ] extrinsic_L5_3 (budget pops=4000 evals=30605 maxopen=26606) +[ ] extrinsic_L5_6 (budget pops=4000 evals=23774 maxopen=19775) +[ ] extrinsic_L5_5 (budget pops=4000 evals=30765 maxopen=26766) +[ ] extrinsic_L5_4 (budget pops=4000 evals=30439 maxopen=26440) +[OK ] extrinsic_L6_1 (solved pops=344 evals=1958 maxopen=1615) +[ ] extrinsic_L5_7 (budget pops=4000 evals=30080 maxopen=26081) +[ ] extrinsic_L5_11 (budget pops=4000 evals=30864 maxopen=26865) +[ ] extrinsic_L5_8 (budget pops=4000 evals=31602 maxopen=27603) +[ ] extrinsic_L5_9 (budget pops=4000 evals=30833 maxopen=26834) +[ ] extrinsic_L5_10 (budget pops=4000 evals=33105 maxopen=29106) +[ ] extrinsic_L6_2 (budget pops=4000 evals=29263 maxopen=25264) +[ ] extrinsic_L6_3 (budget pops=4000 evals=27721 maxopen=23722) +[ ] extrinsic_L6_4 (budget pops=4000 evals=27734 maxopen=23735) +[ ] extrinsic_L6_5 (budget pops=4000 evals=28157 maxopen=24158) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25708 maxopen=21709) +[ ] extrinsic_L6_7 (budget pops=4000 evals=24357 maxopen=20358) +[ ] extrinsic_L6_9 (budget pops=4000 evals=24500 maxopen=20501) +[ ] extrinsic_L6_8 (budget pops=4000 evals=25221 maxopen=21222) +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) -> 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-> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or x x0)).", + "c em", + "=> (em goal12).", + "a x3", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('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) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or x x0)) (not x)).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('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) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or x x0)) (not x))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('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) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or x x0)) (not x))].", + "intro.", + "c x5", + "=> (x5 and_i@type x x5 x4).", + "a and_i", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('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) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or x x0)); (not x).", + "c x5", + "=> (x5 or_il@type not_i@type or_il not_i).", + "a x5", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('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) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); (or x x0).", + "a x3", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('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) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "c x3", + "=> (x3 or_il@type not_i@type p4).", + "a x3", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and [[('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) -> (and 'P 'Q) -> 'P] -> (not x)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x5", + "=> (x5 x p@type x2 p).", + "c x5", + "=> (x5 iff_er@type and_i@type iff_er and_i).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 369, + "actions": [ + "intro.", + "intro.", + "intro.", + "a and_i", + "=> (not x); (not x0).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "c em", + "=> (em goal0@1).", + "a not_e", + "=> (or x 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false]].", + "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)]) -> [[('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) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a or_e", + "=> [(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] -> false]]]; [(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] -> false]]].", + "a 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false].", + "a or_e", + "=> [[(not (not x)) -> x] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [(not (not x)) -> x]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c and_er", + "=> (and_er not_e@type p2@type p3).", + "intro.", + "c x4", + "=> (x4 goal0 or_ir@type x0 or_ir).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4586, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not (not x)) -> x]); [(not (not x)) -> x].", + "a not_i", + "=> [[(not (not x)) -> x] -> false].", + "c em", + "=> (em or_e@type).", + "intro.", + "a not_e", + "=> (not (not (not x))).", + "a not_i", + "=> [(not (not x)) -> false].", + "intro.", + "c x1", + "=> (x1 x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) 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-> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x6", + "=> (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]) (and (and false [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]) (and (and false [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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x0) -> x]) x))].", + "c x3", + "=> (x3 goal).", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (and false [[('P : prop) -> (or 'P (not 'P))] -> false])] (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [(not x) -> x0])] [(not x0) -> x]) x))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (and false [[('P : prop) -> (or 'P (not 'P))] -> false])] (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [(not x) -> x0])] [(not x0) -> x]) x))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (and false [[('P : prop) -> (or 'P (not 'P))] -> false])] (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [(not x) -> x0])] [(not x0) -> x]) x))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (and false [[('P : prop) -> (or 'P (not 'P))] -> false])] (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [(not x) -> x0])] [(not x0) -> x]) x))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4532, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> 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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 x0)]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('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 x0) -> (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) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x0)]])]]].", + "c em", + "=> (em goal).", + "intro.", + "a x2", + "=> (or [(not x0) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not x0))] (not (not x0))); [[(not x0) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not x0))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not x0) -> (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) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x0)]])]]]; [(not (not x0)) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not x0) -> (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) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x0)]])]]].", + "a or_ir", + "=> (not (not x0)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not x0))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not x0))].", + "a exfalso", + "=> false.", + "a x3", + "=> (or 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prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x4", + "=> (x4 and_er@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal15).", + "c x4", + "=> (x4 p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c x5", + "=> (x5 iff_el@type p1@type iff_el p1).", + "c em", + "=> (em or_ir@type).", + "c x4", + "=> (x4 em@type).", + "c x5", + "=> (x5 exfalso@type not_i@type exfalso not_i).", + "c em", + "=> (em p2@type@2).", + "c and_er", + "=> (and_er exfalso@type not_i@type p7).", + "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].", + "c em", + "=> (em goal20)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 584, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "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).", + "intro.", + "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)])].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('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)])]]; [(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 -> 'Q -> (and 'P 'Q)])]].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "a x0", + "=> (and (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) -> 'Q] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]).", + "a and_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "a x0", + "=> (and [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] (and [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]])).", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] (and [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]])) (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] (and [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false))].", + "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 or_e", + "=> [[('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]]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em goal17)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 394, + "actions": [ + "intro.", + 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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 [x -> x0] [x0 -> x1])); (or [x -> x0] [x0 -> x1]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [x -> x0] [x0 -> x1]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [x -> x0] [x0 -> x1]))].", + "intro.", + "a not_i", + "=> [(or [x -> x0] [x0 -> x1]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [x -> x0] [x0 -> x1]) -> false]].", + "a x4", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [x -> x0] [x0 -> x1])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> false]]]; [(or [x -> x0] [x0 -> x1]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x3", + "=> (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) -> ('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) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_ir", + "=> .", + "intro.", + "a x4", + "=> (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] -> [(or [x -> x0] [x0 -> x1]) -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff '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] -> [(or [x -> x0] [x0 -> x1]) -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a x3", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> 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] -> [(or [x -> x0] [x0 -> x1]) -> false]])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> 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] -> [(or [x -> x0] [x0 -> x1]) -> 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] -> [(or [x -> x0] [x0 -> x1]) -> 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] -> [(or [x -> x0] [x0 -> x1]) -> false]])].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> false]].", + "a x3", + "=> (or [x -> x0] [('P : prop) -> (or 'P (not 'P))]); [[x -> x0] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [x -> x0] [x0 -> x1]) -> false]]].", + "c x5", + "=> (x5 x4).", + "a or_ir", + "=> .", + "a x3", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [x -> x0] [x0 -> x1]))] (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [x -> x0] [x0 -> x1]))); [[[('P : 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x3", + "=> (and (and (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [x0 -> x1])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]).", + "a and_i", + "=> (and (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [x0 -> x1])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[(or x x0) -> 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['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[('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) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> 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0000000000000000000000000000000000000000..eaea82b14a3f38347f4e7a6fb1fa14ba7ba15645 --- /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_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_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[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_6 (solved pops=5 evals=14 maxopen=10) +[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=10 evals=28 maxopen=19) +[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_L0_8 (solved pops=6 evals=19 maxopen=14) +[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=19 evals=85 maxopen=67) +[OK ] extrinsic_L0_12 (solved pops=33 evals=228 maxopen=179) +[OK ] extrinsic_L2_1 (solved pops=24 evals=72 maxopen=49) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_6 (solved pops=21 evals=49 maxopen=29) +[OK ] extrinsic_L2_3 (solved pops=37 evals=235 maxopen=199) +[OK ] extrinsic_L2_4 (solved pops=32 evals=173 maxopen=142) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_8 (solved pops=20 evals=66 maxopen=47) +[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=38 evals=249 maxopen=212) +[OK ] extrinsic_L2_12 (solved pops=54 evals=195 maxopen=142) +[OK ] extrinsic_L3_3 (solved pops=12 evals=30 maxopen=19) +[OK ] extrinsic_L3_2 (solved pops=64 evals=391 maxopen=328) +[OK ] extrinsic_L2_5 (solved pops=116 evals=573 maxopen=458) +[OK ] extrinsic_L3_4 (solved pops=30 evals=209 maxopen=159) +[OK ] extrinsic_L3_5 (solved pops=30 evals=206 maxopen=156) +[OK ] extrinsic_L3_6 (solved pops=94 evals=451 maxopen=358) +[OK ] extrinsic_L2_2 (solved pops=194 evals=874 maxopen=681) +[OK ] extrinsic_L3_11 (solved pops=97 evals=496 maxopen=397) +[OK ] extrinsic_L3_12 (solved pops=107 evals=551 maxopen=445) +[OK ] extrinsic_L3_13 (solved pops=10 evals=28 maxopen=19) +[OK ] extrinsic_L3_14 (solved pops=17 evals=58 maxopen=42) +[OK ] extrinsic_L3_15 (solved pops=136 evals=749 maxopen=614) +[OK ] extrinsic_L3_16 (solved pops=38 evals=160 maxopen=123) +[OK ] extrinsic_L3_17 (solved pops=67 evals=427 maxopen=342) +[OK ] extrinsic_L3_18 (solved pops=99 evals=692 maxopen=573) +[OK ] extrinsic_L3_7 (solved pops=1662 evals=7926 maxopen=6265) +[ ] extrinsic_L2_13 (budget pops=4000 evals=21817 maxopen=17818) +[OK ] extrinsic_L3_9 (solved pops=3508 evals=18562 maxopen=15032) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25347 maxopen=21348) +[OK ] extrinsic_L3_23 (solved pops=68 evals=386 maxopen=319) +[ ] extrinsic_L3_10 (budget pops=4000 evals=21190 maxopen=17191) +[ ] extrinsic_L3_19 (budget pops=4000 evals=20456 maxopen=16457) +[OK ] extrinsic_L3_25 (solved pops=806 evals=5618 maxopen=4793) +[ ] extrinsic_L3_20 (budget pops=4000 evals=20408 maxopen=16409) +[ ] extrinsic_L3_21 (budget pops=4000 evals=20516 maxopen=16517) +[ ] extrinsic_L3_24 (budget pops=4000 evals=23530 maxopen=19531) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19636 maxopen=15637) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25703 maxopen=21704) +[ ] extrinsic_L3_27 (budget pops=4000 evals=27145 maxopen=23146) +[OK ] extrinsic_L4_3 (solved pops=1029 evals=4902 maxopen=3874) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25172 maxopen=21173) +[ ] extrinsic_L4_1 (budget pops=4000 evals=22776 maxopen=18777) +[ ] extrinsic_L4_2 (budget pops=4000 evals=32701 maxopen=28702) +[ ] extrinsic_L4_4 (budget pops=4000 evals=28913 maxopen=24914) +[ ] extrinsic_L4_5 (budget pops=4000 evals=31612 maxopen=27613) +[ ] extrinsic_L3_29 (budget pops=4000 evals=24443 maxopen=20444) +[ ] extrinsic_L4_6 (budget pops=4000 evals=28855 maxopen=24856) +[OK ] extrinsic_L4_12 (solved pops=291 evals=1444 maxopen=1151) +[ ] extrinsic_L4_7 (budget pops=4000 evals=24671 maxopen=20672) +[ ] extrinsic_L4_8 (budget pops=4000 evals=23788 maxopen=19789) +[ ] extrinsic_L4_9 (budget pops=4000 evals=24556 maxopen=20557) +[ ] extrinsic_L4_10 (budget pops=4000 evals=28594 maxopen=24595) +[ ] extrinsic_L4_13 (budget pops=4000 evals=28906 maxopen=24907) +[ ] extrinsic_L4_14 (budget pops=4000 evals=28589 maxopen=24590) +[ ] extrinsic_L4_11 (budget pops=4000 evals=35336 maxopen=31337) +[ ] extrinsic_L5_1 (budget pops=4000 evals=21192 maxopen=17193) +[ ] extrinsic_L5_2 (budget pops=4000 evals=22450 maxopen=18451) +[ ] extrinsic_L5_6 (budget pops=4000 evals=25399 maxopen=21400) +[ ] extrinsic_L5_3 (budget pops=4000 evals=21978 maxopen=17979) +[ ] extrinsic_L5_5 (budget pops=4000 evals=28350 maxopen=24351) +[ ] extrinsic_L5_4 (budget pops=4000 evals=21626 maxopen=17627) +[OK ] extrinsic_L6_1 (solved pops=48 evals=315 maxopen=268) +[ ] extrinsic_L5_7 (budget pops=4000 evals=24978 maxopen=20979) +[ ] extrinsic_L5_8 (budget pops=4000 evals=27229 maxopen=23230) +[ ] extrinsic_L5_9 (budget pops=4000 evals=21383 maxopen=17384) +[ ] extrinsic_L5_11 (budget pops=4000 evals=55866 maxopen=51867) +[ ] extrinsic_L5_10 (budget pops=4000 evals=22572 maxopen=18573) +[ ] extrinsic_L6_2 (budget pops=4000 evals=23167 maxopen=19168) +[OK ] extrinsic_L6_6 (solved pops=2190 evals=10870 maxopen=8681) +[ ] extrinsic_L6_3 (budget pops=4000 evals=23687 maxopen=19688) +[ ] extrinsic_L6_4 (budget pops=4000 evals=26696 maxopen=22697) +[ ] extrinsic_L6_7 (budget pops=4000 evals=22385 maxopen=18386) +[ ] extrinsic_L6_5 (budget pops=4000 evals=23115 maxopen=19116) +[ ] extrinsic_L6_9 (budget pops=4000 evals=27880 maxopen=23881) +[ ] extrinsic_L6_8 (budget pops=4000 evals=23338 maxopen=19339) +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/bf_extrinsic-95_mid.json +Solved 52/94 in 2126.9s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/summary.json b/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..75424899b8dcfa8f4febe59b487ac3f2053ee755 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_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": 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[('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 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'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=7 evals=17 maxopen=11) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_7 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L0_8 (solved pops=6 evals=19 maxopen=14) +[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_12 (solved pops=26 evals=168 maxopen=126) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L1_3 (solved pops=10 evals=24 maxopen=15) +[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_2 (solved pops=10 evals=24 maxopen=15) +[OK ] extrinsic_L2_1 (solved pops=30 evals=115 maxopen=86) +[OK ] extrinsic_L0_14 (solved pops=29 evals=157 maxopen=129) +[OK ] extrinsic_L2_3 (solved pops=30 evals=173 maxopen=144) +[OK ] extrinsic_L2_4 (solved pops=29 evals=153 maxopen=125) +[OK ] extrinsic_L2_7 (solved pops=13 evals=30 maxopen=18) +[OK ] extrinsic_L2_6 (solved pops=21 evals=46 maxopen=26) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=19 evals=76 maxopen=58) +[OK ] extrinsic_L2_10 (solved pops=20 evals=61 maxopen=42) +[OK ] extrinsic_L2_8 (solved pops=33 evals=163 maxopen=131) +[OK ] extrinsic_L2_12 (solved pops=39 evals=142 maxopen=104) +[OK ] extrinsic_L3_1 (solved pops=28 evals=167 maxopen=140) +[OK ] extrinsic_L3_3 (solved pops=14 evals=34 maxopen=21) +[OK ] extrinsic_L3_4 (solved pops=30 evals=209 maxopen=159) +[OK ] extrinsic_L3_5 (solved pops=30 evals=206 maxopen=156) +[OK ] extrinsic_L3_2 (solved pops=65 evals=354 maxopen=290) +[OK ] extrinsic_L2_5 (solved pops=141 evals=650 maxopen=510) +[OK ] extrinsic_L3_6 (solved pops=123 evals=574 maxopen=452) +[OK ] extrinsic_L2_2 (solved pops=262 evals=1168 maxopen=907) +[OK ] extrinsic_L3_11 (solved pops=135 evals=657 maxopen=520) +[OK ] extrinsic_L3_12 (solved pops=211 evals=962 maxopen=752) +[OK ] extrinsic_L3_13 (solved pops=15 evals=87 maxopen=73) +[OK ] extrinsic_L3_14 (solved pops=23 evals=104 maxopen=82) +[OK ] extrinsic_L3_15 (solved pops=250 evals=1222 maxopen=973) +[OK ] extrinsic_L3_16 (solved pops=41 evals=196 maxopen=156) +[OK ] extrinsic_L3_17 (solved pops=71 evals=415 maxopen=326) +[OK ] extrinsic_L3_18 (solved pops=59 evals=421 maxopen=342) +[OK ] extrinsic_L3_7 (solved pops=2502 evals=14492 maxopen=11991) +[ ] extrinsic_L2_13 (budget pops=4000 evals=22982 maxopen=18983) +[OK ] extrinsic_L3_9 (solved pops=3995 evals=21917 maxopen=17900) +[ ] extrinsic_L3_8 (budget pops=4000 evals=27785 maxopen=23786) +[ ] extrinsic_L3_10 (budget pops=4000 evals=21316 maxopen=17317) +[OK ] extrinsic_L3_23 (solved pops=110 evals=573 maxopen=464) +[ ] extrinsic_L3_19 (budget pops=4000 evals=22409 maxopen=18410) +[OK ] extrinsic_L3_25 (solved pops=1285 evals=8767 maxopen=7463) +[ ] extrinsic_L3_20 (budget pops=4000 evals=21979 maxopen=17980) +[ ] extrinsic_L3_21 (budget pops=4000 evals=22170 maxopen=18171) +[ ] extrinsic_L3_24 (budget pops=4000 evals=24763 maxopen=20764) +[ ] extrinsic_L3_22 (budget pops=4000 evals=21423 maxopen=17424) +[ ] extrinsic_L3_26 (budget pops=4000 evals=29085 maxopen=25086) +[ ] extrinsic_L3_27 (budget pops=4000 evals=29829 maxopen=25830) +[ ] extrinsic_L4_1 (budget pops=4000 evals=24011 maxopen=20012) +[OK ] extrinsic_L4_3 (solved pops=1965 evals=12529 maxopen=10565) +[ ] extrinsic_L3_28 (budget pops=4000 evals=29577 maxopen=25578) +[ ] extrinsic_L4_2 (budget pops=4000 evals=33693 maxopen=29694) +[ ] extrinsic_L4_4 (budget pops=4000 evals=32951 maxopen=28952) +[ ] extrinsic_L3_29 (budget pops=4000 evals=27770 maxopen=23771) +[ ] extrinsic_L4_6 (budget pops=4000 evals=31180 maxopen=27181) +[ ] extrinsic_L4_5 (budget pops=4000 evals=36026 maxopen=32027) +[OK ] extrinsic_L4_12 (solved pops=519 evals=2453 maxopen=1932) +[ ] extrinsic_L4_7 (budget pops=4000 evals=27456 maxopen=23457) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26229 maxopen=22230) +[ ] extrinsic_L4_9 (budget pops=4000 evals=27676 maxopen=23677) +[ ] extrinsic_L4_10 (budget pops=4000 evals=29064 maxopen=25065) +[ ] extrinsic_L4_11 (budget pops=4000 evals=34203 maxopen=30204) +[ ] extrinsic_L4_13 (budget pops=4000 evals=30334 maxopen=26335) +[ ] extrinsic_L4_14 (budget pops=4000 evals=31691 maxopen=27692) +[ ] extrinsic_L5_1 (budget pops=4000 evals=23134 maxopen=19135) +[ ] extrinsic_L5_2 (budget pops=4000 evals=24669 maxopen=20670) +[ ] extrinsic_L5_3 (budget pops=4000 evals=24992 maxopen=20993) +[ ] extrinsic_L5_6 (budget pops=4000 evals=29206 maxopen=25207) +[ ] extrinsic_L5_4 (budget pops=4000 evals=24572 maxopen=20573) +[ ] extrinsic_L5_5 (budget pops=4000 evals=32601 maxopen=28602) +[OK ] extrinsic_L6_1 (solved pops=58 evals=381 maxopen=324) +[ ] extrinsic_L5_7 (budget pops=4000 evals=29163 maxopen=25164) +[ ] extrinsic_L5_8 (budget pops=4000 evals=28615 maxopen=24616) +[ ] extrinsic_L5_9 (budget pops=4000 evals=24282 maxopen=20283) +[ ] extrinsic_L5_11 (budget pops=4000 evals=58329 maxopen=54330) +[ ] extrinsic_L5_10 (budget pops=4000 evals=25438 maxopen=21439) +[ ] extrinsic_L6_2 (budget pops=4000 evals=55168 maxopen=51169) +[OK ] extrinsic_L6_6 (solved pops=3689 evals=23554 maxopen=19866) +[ ] extrinsic_L6_3 (budget pops=4000 evals=54671 maxopen=50672) +[ ] extrinsic_L6_7 (budget pops=4000 evals=24736 maxopen=20737) +[ ] extrinsic_L6_4 (budget pops=4000 evals=68162 maxopen=64163) +[ ] extrinsic_L6_5 (budget pops=4000 evals=43527 maxopen=39528) +[ ] extrinsic_L6_9 (budget pops=4000 evals=28872 maxopen=24873) +[ ] extrinsic_L6_8 (budget pops=4000 evals=26251 maxopen=22252) +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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"max_open": 39665, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..7e87d2e47d78d5351aebcb2f1afb27d1219f77d6 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/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_2 (solved pops=7 evals=18 maxopen=12) +[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_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_5 (solved pops=9 evals=21 maxopen=13) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_7 (solved pops=12 evals=34 maxopen=23) +[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=8 evals=25 maxopen=18) +[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=15 evals=44 maxopen=30) +[OK ] extrinsic_L2_1 (solved pops=23 evals=56 maxopen=34) +[OK ] extrinsic_L2_4 (solved pops=19 evals=68 maxopen=50) +[OK ] extrinsic_L2_3 (solved pops=21 evals=72 maxopen=52) +[OK ] extrinsic_L2_7 (solved pops=9 evals=22 maxopen=14) +[OK ] extrinsic_L2_6 (solved pops=19 evals=44 maxopen=26) +[OK ] extrinsic_L2_8 (solved pops=15 evals=40 maxopen=26) +[OK ] extrinsic_L2_9 (solved pops=14 evals=50 maxopen=37) +[OK ] extrinsic_L0_12 (solved pops=60 evals=328 maxopen=252) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L3_1 (solved pops=17 evals=61 maxopen=45) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L2_12 (solved pops=49 evals=171 maxopen=123) +[OK ] extrinsic_L3_4 (solved pops=23 evals=149 maxopen=106) +[OK ] extrinsic_L3_2 (solved pops=57 evals=305 maxopen=249) +[OK ] extrinsic_L2_5 (solved pops=101 evals=515 maxopen=415) +[OK ] extrinsic_L3_5 (solved pops=25 evals=150 maxopen=105) +[OK ] extrinsic_L3_6 (solved pops=84 evals=378 maxopen=295) +[OK ] extrinsic_L2_2 (solved pops=171 evals=775 maxopen=605) +[OK ] extrinsic_L3_11 (solved pops=85 evals=390 maxopen=303) +[OK ] extrinsic_L3_12 (solved pops=98 evals=485 maxopen=388) +[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=104 evals=563 maxopen=460) +[OK ] extrinsic_L3_16 (solved pops=33 evals=99 maxopen=67) +[OK ] extrinsic_L3_17 (solved pops=63 evals=357 maxopen=276) +[OK ] extrinsic_L3_18 (solved pops=68 evals=478 maxopen=390) +[OK ] extrinsic_L3_7 (solved pops=929 evals=4584 maxopen=3656) +[OK ] extrinsic_L3_9 (solved pops=2905 evals=15771 maxopen=12844) +[ ] extrinsic_L2_13 (budget pops=4000 evals=21302 maxopen=17303) +[ ] extrinsic_L3_8 (budget pops=4000 evals=27224 maxopen=23225) +[OK ] extrinsic_L3_23 (solved pops=58 evals=304 maxopen=247) +[ ] extrinsic_L3_10 (budget pops=4000 evals=20712 maxopen=16713) +[ ] extrinsic_L3_19 (budget pops=4000 evals=20235 maxopen=16236) +[ ] extrinsic_L3_20 (budget pops=4000 evals=19575 maxopen=15576) +[OK ] extrinsic_L3_25 (solved pops=909 evals=6272 maxopen=5344) +[ ] extrinsic_L3_22 (budget pops=4000 evals=19173 maxopen=15174) +[ ] extrinsic_L3_21 (budget pops=4000 evals=20336 maxopen=16337) +[ ] extrinsic_L3_24 (budget pops=4000 evals=23523 maxopen=19524) +[ ] extrinsic_L3_26 (budget pops=4000 evals=27623 maxopen=23624) +[ ] extrinsic_L3_27 (budget pops=4000 evals=28952 maxopen=24953) +[ ] extrinsic_L4_1 (budget pops=4000 evals=22185 maxopen=18186) +[OK ] extrinsic_L4_3 (solved pops=1140 evals=5468 maxopen=4329) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26799 maxopen=22800) +[ ] extrinsic_L4_2 (budget pops=4000 evals=31619 maxopen=27620) +[ ] extrinsic_L4_4 (budget pops=4000 evals=29630 maxopen=25631) +[ ] extrinsic_L3_29 (budget pops=4000 evals=25327 maxopen=21328) +[ ] extrinsic_L4_6 (budget pops=4000 evals=28926 maxopen=24927) +[ ] extrinsic_L4_5 (budget pops=4000 evals=32712 maxopen=28713) +[ ] extrinsic_L4_7 (budget pops=4000 evals=25623 maxopen=21624) +[OK ] extrinsic_L4_12 (solved pops=353 evals=1675 maxopen=1320) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25927 maxopen=21928) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26431 maxopen=22432) +[ ] extrinsic_L4_10 (budget pops=4000 evals=28714 maxopen=24715) +[ ] extrinsic_L4_13 (budget pops=4000 evals=28690 maxopen=24691) +[ ] extrinsic_L4_11 (budget pops=4000 evals=35435 maxopen=31436) +[ ] extrinsic_L4_14 (budget pops=4000 evals=29688 maxopen=25689) +[ ] extrinsic_L5_1 (budget pops=4000 evals=20249 maxopen=16250) +[ ] extrinsic_L5_2 (budget pops=4000 evals=21595 maxopen=17596) +[ ] extrinsic_L5_3 (budget pops=4000 evals=21358 maxopen=17359) +[ ] extrinsic_L5_6 (budget pops=4000 evals=27621 maxopen=23622) +[ ] extrinsic_L5_5 (budget pops=4000 evals=31111 maxopen=27112) +[ ] extrinsic_L5_4 (budget pops=4000 evals=20286 maxopen=16287) +[OK ] extrinsic_L6_1 (solved pops=36 evals=202 maxopen=167) +[ ] extrinsic_L5_7 (budget pops=4000 evals=25235 maxopen=21236) +[ ] extrinsic_L5_8 (budget pops=4000 evals=28345 maxopen=24346) +[ ] extrinsic_L5_9 (budget pops=4000 evals=20396 maxopen=16397) +[ ] extrinsic_L5_11 (budget pops=4000 evals=55286 maxopen=51287) +[ ] extrinsic_L5_10 (budget pops=4000 evals=22542 maxopen=18543) +[OK ] extrinsic_L6_6 (solved pops=1183 evals=5953 maxopen=4771) +[ ] extrinsic_L6_2 (budget pops=4000 evals=22689 maxopen=18690) +[ ] extrinsic_L6_4 (budget pops=4000 evals=28916 maxopen=24917) +[ ] extrinsic_L6_3 (budget pops=4000 evals=23492 maxopen=19493) +[ ] extrinsic_L6_7 (budget pops=4000 evals=21521 maxopen=17522) +[ ] extrinsic_L6_5 (budget pops=4000 evals=22462 maxopen=18463) +[ ] extrinsic_L6_8 (budget pops=4000 evals=25504 maxopen=21505) +[ ] extrinsic_L6_9 (budget pops=4000 evals=43664 maxopen=39665) +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 : 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-> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and false [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]))]]])))).", + "a x5", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))])]] (and (and [('P : prop) -> ['P -> false] -> (not 'P)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and false [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]))]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and false [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]))]]])) (and [('P : prop) -> ['P 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-> ['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 x1", + "=> (or (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]) -> [[('P : prop) -> ('Q : prop) -> ('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) -> '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 x1", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (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) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]])].", + "a x1", + "=> (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) -> (not 'P) -> '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] -> [[('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) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [(not [('P : prop) -> 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-> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> [(not (not 'A)) -> 'A]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> [(not (not 'A)) -> 'A]])]].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> [(not (not 'A)) -> 'A]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> [(not (not 'A)) -> 'A]])]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not 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-> 'P]] -> false]))) -> (iff (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))) false)].", + "intro.", + "c em", + "=> (em p@type).", + "a x4", + "=> [(not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))) -> false]; [false -> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])))].", + "a x5", + "=> (iff false (not (or [[('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": 324, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em exfalso@type).", + 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not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> 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].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> '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.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] false).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; false.", + "a x1", + "=> (and [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] [[('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) -> ('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] -> [[('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", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or '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 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]].", + "c em", + "=> (em iff_i@type).", + "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.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x3", + "=> (or [('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] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_ir", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "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]])].", + "c em", + "=> (em p@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 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 x3", + "=> (or [('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] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]); [[('P 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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]) -> [[('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": 350, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x).", + "a x1", + "=> (not x0).", + "a not_i", + "=> [x0 -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x0)); (not x0).", + "a not_i", + "=> [(not x0) -> false].", + "intro.", + "c x1", + "=> (x1 x4).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not x0) -> false]); [(not x0) -> false].", + "c not_e", + "=> (not_e x0 x4 x3).", + "c not_e", + "=> (not_e x p x2).", + "a not_i", 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]].", + "a x1", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('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) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (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] -> (not 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) -> (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))] [('P : prop) -> (or 'P (not 'P))])].", + "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 [('P : prop) -> (or 'P (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) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em goal0).", + "intro.", + "c em", + "=> (em p1@type).", + "a or_il", + "=> .", + "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]) -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])]]; [(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) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])]].", + "a x2", + "=> (or (or [('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] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])]); [(or [('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] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('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] -> (or [('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] -> [(not [('P : 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(and 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]].", + "a x4", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal25).", + "a x4", + "=> (and (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 486, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not x0) -> x]); [(not x0) -> x].", + "a not_i", + "=> [[(not x0) -> x] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal28)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 395, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[(not x) -> x0] -> [(not x0) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[(not x) -> x0] -> [(not x0) -> x]]].", + "intro.", + "a x1", + "=> (iff [(not x0) -> x] [(not x) -> x0]).", + "a iff_i", + "=> [[(not x0) -> x] -> [(not x) -> x0]]; [[(not x) -> x0] -> [(not x0) -> x]].", + "intro.", + "a x1", + "=> (iff x0 (not x)).", + "a iff_i", + "=> [x0 -> (not x)]; [(not x) -> x0].", + "a x1", + "=> (iff (not x) x0).", + "a iff_i", + "=> [(not x) -> x0]; [x0 -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not 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prop) -> ('Q : prop) -> ('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 x0))]]]; [x0 -> [[('P : prop) -> ('Q : prop) -> ('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 x0))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff '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])) x0)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff '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])) x0)].", + "a x5", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (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]))); [(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)] -> (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])) x0)]]; [(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)] -> (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])) x0)]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2257, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not [(not x) -> x0]).", + "a not_i", + "=> [[(not x) -> x0] -> false].", + "intro.", + "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)])].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[(not x) -> x0] -> false]); [[(not x) -> x0] -> 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 not_e", + "=> (not (not x0)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not x0))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not x0))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not x0))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not x0))].", + "c x5", + "=> (x5 or_il@type x1@type or_il x1).", + "c x5", + "=> (x5 and_er@type or_il@type and_er or_il).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]].", + "c x5", + "=> (x5 x1@type em@type x4 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['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]].", + "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]]; [(not [('P : prop) -> ('Q : prop) -> ('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 x1", + "=> (or (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]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x1", + "=> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]).", + "a x2", + "=> (or [x -> (not x)] x); [[x -> (not x)] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])]; [x -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])].", + "c x1", + "=> (x1 x x0).", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a x2", + "=> (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] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x1", + "=> (x1 x x0).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a x1", + "=> (not [false -> (not false)]).", + "a x1", + "=> (not [(not [false -> (not false)]) -> (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 false)]) -> (not (not [false -> (not false)]))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))])].", + "c em", + "=> (em goal).", + "a x2", + "=> (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) -> (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) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))])]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))])]].", + "a or_ir", + "=> .", + "a x1", + "=> (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] -> (not [(not [false -> (not false)]) -> (not (not [false -> (not 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])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))])]])]).", + "a exfalso", + "=> false.", + "a x2", + "=> (or [[x -> (not x)] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])] (not [x -> (not x)])); [[[x -> (not x)] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])] -> false]; [(not [x -> (not x)]) -> false].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 851, + "actions": [ + "intro.", + "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].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x1", + "=> (x1 and_i@type).", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "intro.", + "c x1", + "=> (x1 or_ir@type).", + "c x1", + "=> (x1 goal6).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x1", + "=> (x1 p@type@2).", + "c x1", + "=> (x1 goal9).", + "c em", + "=> (em p2@type@2).", + "c x1", + "=> (x1 not_e@type).", + "c em", + "=> (em and_er@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x3", + "=> (and false (not x)).", + "a and_i", + "=> false; (not x).", + "a x3", + "=> (and false (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))).", + "a x3", + "=> (and (and false (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))) x).", + "c em", + "=> (em goal16).", + "c x1", + "=> (x1 p7@type).", + "c em", + "=> (em p8@type).", + "a x3", + "=> (and (and (and false (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))) x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x3", + "=> (and (and (and (and false (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))) x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 651, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> x]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> x].", + "intro.", + "a x1", + "=> (and [('P : prop) -> (or 'P (not 'P))] x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> (or 'P (not 'P))] x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] 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] -> (and [('P : prop) -> (or 'P (not 'P))] x)]]]; [(not [('P : prop) -> 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]])].", + "a x2", + "=> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]])]).", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]])])).", + "c em", + "=> (em not_e@type).", + "a and_i", + "=> (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]])]).", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]])] (and x [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]])])).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false false).", + "c em", + "=> (em or_e@type).", + "a x3", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and false false)).", + "a and_i", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]); (and false false).", + "a x1", + "=> (and [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a x1", + "=> (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] -> (and [('P : prop) -> (or 'P (not 'P))] x)]]] (and [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (or 'P (not 'P))] x)]]]; (and [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a x2", + "=> (and (and false 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] -> (and [('P : prop) -> (or 'P (not 'P))] x)]]]).", + "a and_i", + "=> (and false 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] -> (and [('P : prop) -> (or 'P (not 'P))] x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and false false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and false false)].", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and false false)]).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": 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not_i", + "=> [(not false) -> 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].", + "intro.", + "a not_e", + "=> (not (not (not false))); (not (not false)).", + "a not_i", + "=> [(not (not false)) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x5" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 471, + "actions": [ + "intro.", + "intro.", + "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].", + "intro.", + "a not_e", + "=> (not false); false.", + "a not_i", 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'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]] -> false].", + "intro.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> false]; [[(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]] -> false].", + "c x2", + "=> (x2 p4@type@2 p3@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4991, + "actions": [ + "intro.", + "intro.", + "a or_il", + "=> [x -> x0].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c em", + "=> (em false).", + "c x2", + "=> (x2 p1@type).", + "c x2", + "=> (x2 p0@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 goal0@2).", + "a x3", + "=> (or (not [x0 -> x]) (or [x0 -> x] (not [x0 -> x]))); [(not [x0 -> x]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(or [x0 -> x] (not [x0 -> x])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_ir", + "=> .", + "c x2", + "=> (x2 exfalso@type).", + "a or_e", + "=> [[x0 -> x] -> [(not [x0 -> x]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [x0 -> x]) -> [(not [x0 -> x]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a x3", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 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['Q -> 'P]] -> (not (not (not [false -> ('P : prop) -> 'P])))]].", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [false -> ('P : prop) -> 'P])))]]]; [(not (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [false -> ('P : prop) -> 'P])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 exfalso@type x5 x3).", + "c x2", + "=> (x2 exfalso@type x5 exfalso).", + "c x3", + "=> (x3 p5 goal5).", + "c p6", + "=> (p6 x2).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3010, + "actions": [ + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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-> [false -> false]]].", + "c em", + "=> (em em@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 649, + "actions": [ + "intro.", + "intro.", + "a iff_i", + "=> [(not [x -> x0]) -> (and x (not x0))]; [(and x (not x0)) -> (not [x -> x0])].", + "intro.", + "a and_i", + "=> x; (not x0).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x2", + "=> (x2 goal0@1).", + "a or_e", + "=> [(not [x -> x0]) -> false]; [(not (not [x -> x0])) -> false].", + "intro.", + "a not_e", + "=> (not (not [x -> x0])).", + "a or_e", + "=> [(not [x -> x0]) -> (not (not [x -> x0]))]; [(not (not [x -> x0])) -> (not (not [x -> x0]))].", + "intro.", + "c x2", + "=> (x2 goal5).", + "a not_i", + "=> [(not [x -> x0]) -> false].", + "c x2", + "=> (x2 goal0@2).", + "c x2", + "=> (x2 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-> 'Q])].", + "intro.", + "a x3", + "=> (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x3", + "=> (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "a x2", + "=> (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))).", + "a x4", + "=> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))].", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))].", + "c em", + "=> (em goal17).", + "a or_e", + "=> [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]]; [(not (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]].", + "a x2", + "=> (and [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]] x).", + "a and_i", + "=> [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]]; x.", + "a x3", + "=> (and [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]] [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]]).", + "a or_e", + "=> [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]] [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]])]; [(not (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (iff (not [x -> x0]) (and x (not x0)))) (not [x -> x0]))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] (and x (not x0)))]] [(and (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and x [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and 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('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 611, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "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].", + "intro.", + "a x3", + "=> (and false [false -> ('P : prop) -> 'P]).", + "a and_i", + "=> false.", + "a x3", + "=> (and false x).", + "a and_i", + "=> false; x.", + "a exfalso", + "=> false.", + "a x3", + "=> (and false x0).", + "a x3", + "=> (and (and false x0) [x0 -> x1]).", + "a x3", + "=> (and (and (and false x0) [x0 -> x1]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x3", + "=> (and (and 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [false -> ('P : prop) -> 'P])) x1) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]).", + "a x3", + "=> (and (and (and (and (and (and (and (and (and false x0) [x0 -> x1]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [false -> ('P : prop) -> 'P])) x1) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) x0).", + "a and_i", + "=> (and (and (and (and (and (and (and (and false x0) [x0 -> x1]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [false -> ('P : prop) -> 'P])) x1) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]).", + "a x3", + "=> (and (and (and (and (and (and (and (and (and false x0) [x0 -> x1]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [false -> ('P : prop) -> 'P])) x1) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) x0).", + "c em", + "=> (em x).", + "a x3", + "=> (and (and (and (and (and (and (and (and (and (and false x0) [x0 -> x1]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [false -> ('P : prop) -> 'P])) x1) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) x0) x1).", + "c em", + "=> (em goal9).", + "a and_i", + "=> (and (and (and (and (and (and (and (and (and false x0) [x0 -> x1]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [false -> ('P : prop) -> 'P])) x1) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) x0); x1.", + "a and_i", + "=> (and (and (and (and (and (and (and (and false x0) [x0 -> x1]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [false -> ('P : prop) -> 'P])) x1) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and false x) -> false]; [(not (and false x)) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 526, + "actions": [ + "intro.", + "intro.", + "a exfalso", + 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'P] false))).", + "a and_i", + "=> x0; (and false (and [false -> ('P : prop) -> 'P] false)).", + "a exfalso", + "=> false.", + "a x2", + "=> (and [false -> ('P : prop) -> 'P] false).", + "a x3", + "=> (and [(not false) -> false] (and [false -> ('P : prop) -> 'P] false)).", + "a and_i", + "=> [(not false) -> false]; (and [false -> ('P : prop) -> 'P] false).", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not false) -> false]).", + "a x2", + "=> (and x0 (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not false) -> false])).", + "a x3", + "=> (and x0 (and x0 (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not false) -> false]))).", + "a and_i", + "=> x0; (and x0 (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(not false) -> false])).", + "a x3", + "=> (and [('P : prop) -> 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'P 'Q)] -> false]].", + "c and_er", + "=> (and_er and_i@type not_i@type p).", + "c em", + "=> (em p1@type@2).", + "intro.", + "c em", + "=> (em p0@type).", + "c x3", + "=> (x3 goal8 iff_i@type iff_i).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c x3", + "=> (x3 x1 or_il@type or_il).", + "c x2", + "=> (x2 p4@type p1@type p4 p1).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "c em", + "=> (em iff_i@type).", + "c x2", + "=> (x2 iff_i@type p8@type iff_i p8).", + "intro.", + "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) -> ('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] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "c em", + "=> (em goal0@1).", + "a exfalso", + "=> false.", + "c and_er", + "=> (and_er iff_i@type p8@type p9).", + "c p2", + "=> (p2 or_ir@type x4).", + "c x4", + "=> (x4 x3)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 498, + "actions": [ + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x3", + "=> (and false 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].", + "c em", + "=> (em em@type).", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x2", + "=> (iff false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a iff_i", + "=> [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 x3", + "=> (and [false -> [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]] [x0 -> x1]).", + "a and_i", + "=> [false -> [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 740, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_il", + "=> [x -> x0].", + "intro.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x0]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> x0].", + "intro.", + "a x3", + "=> (and x0 [x -> x0]).", + "a x3", + "=> (and (and x0 [x -> x0]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> (and x0 [x -> x0]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and x0 [x -> x0])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and x0 [x -> x0])].", + "intro.", + "a x4", + "=> (and (and x0 [x -> x0]) x0).", + "a x4", + "=> (and (and (and x0 [x -> x0]) x0) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a x4", + "=> (and false (and (and x0 [x -> x0]) x0)).", + "a x4", + "=> (and (and false (and (and x0 [x -> x0]) x0)) (and (and x0 [x -> x0]) x0)).", + "a x3", + "=> (and (and (and false (and (and x0 [x -> x0]) x0)) (and (and x0 [x -> x0]) x0)) (and (and false (and (and x0 [x -> x0]) x0)) (and (and x0 [x -> x0]) x0))).", + "a x4", + "=> (and (and (and (and false (and (and x0 [x -> x0]) x0)) (and (and x0 [x -> x0]) x0)) (and (and false (and (and x0 [x -> x0]) x0)) (and (and x0 [x -> x0]) x0))) (and (and (and x0 [x -> x0]) x0) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a x3", + "=> (and (and (and (and (and 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[[('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]].", + "intro.", + "intro.", + "c x6", + "=> (x6 or_il@type or_ir@type or_il or_ir).", + "a x5", + "=> (not (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el or_il@type or_ir@type p0).", + "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 goal16)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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-> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (and false false).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false (and false false)).", + "a and_i", + "=> false; (and false 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 x0", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x0", + "=> (and (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x0", + "=> (and (and (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 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'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 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) -> ['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] -> (not [('P : prop) -> ['P -> false] -> (not '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].", + "intro.", + "a not_e", + "=> (not x0); x0.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x0)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not x0)].", + "intro.", + "a not_i", + "=> [x0 -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x0 -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [x0 -> false]].", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x0 -> 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] -> [x0 -> 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 x3", + "=> (or x2 (not [('P : prop) -> ['P -> false] -> (not 'P)])); [x2 -> [[('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) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_ir", + "=> (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 x3", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [x0 -> 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] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [[x0 -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "c em", + "=> (em and_el@type).", + "a or_ir", + "=> [x0 -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [x0 -> false]].", + "a x4", + "=> (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]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> false]]].", + "c em", + "=> (em goal8).", + "a or_il", + "=> .", + "a x3", + "=> (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] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> 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] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> 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) -> ('R : prop) -> (or 'P '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) -> ['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))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P '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) -> ['P -> false] -> (not 'P)])]]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 326, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "a or_il", + "=> x0.", + "a or_e", + "=> [x1 -> x0].", + "intro.", + "a or_e", + "=> [x1 -> x0].", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [x1 -> false].", + 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[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('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] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('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] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]])].", + "intro.", + "a and_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('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] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "c em", + "=> (em goal0).", + "a exfalso", + "=> false.", + "a x2", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]] false).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]] false)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]] false)].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('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] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]] false)]].", + "c em", + "=> (em goal13).", + "intro.", + "a or_e", + "=> [(and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('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] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]] false)]]; [(not (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('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] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]] false)]].", + "a exfalso", + "=> false.", + "a x4", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x2", + "=> (and [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x4", + "=> false.", + "a not_e", + "=> (not (or x [x0 -> x1])); (or x [x0 -> x1]).", + "a not_i", + "=> [(or x [x0 -> x1]) -> false].", + "intro.", + "a x4", + "=> false.", + "a x4", + "=> false.", + "a or_e", + "=> [x -> false]; [[x0 -> x1] -> false].", + "intro.", + "a x4", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a x7", + "=> false.", + "a x7", + "=> false.", + "a x4", + "=> false.", + "a exfalso", + "=> false.", + "a x7", + "=> false.", + "c em", + "=> (em x1).", + "a x7", + "=> false.", + "a x7", + "=> false.", + "a x7", + "=> false.", + "a x7", + "=> false.", + "a x7", + "=> false.", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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[(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "a x3", + "=> false.", + "c not_e", + "=> (not_e exfalso@type x5 exfalso).", + "c x4", + "=> (x4 goal17).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [(not (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]]]; [(not (not [false -> ('P : prop) -> 'P])) -> [(not (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]]].", + "intro.", + "c x4", + "=> (x4 p@type@2).", + "intro.", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "c not_e", + "=> (not_e goal3 x7 x5).", + "c em", + "=> (em not_i@type).", + "a x3", + "=> .", + "intro.", + "intro.", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 404, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "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].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a x5", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a not_e", + "=> (not (or x [x0 -> x1])); (or x [x0 -> x1]).", + "a not_i", + "=> [(or x [x0 -> x1]) -> false].", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> [(or x [x0 -> x1]) -> false]]; [(not false) -> [(or x [x0 -> x1]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [(or x [x0 -> x1]) -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [false -> [(or x [x0 -> x1]) -> false]]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [(or x [x0 -> x1]) -> false]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [(or x [x0 -> x1]) -> false]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [(or x [x0 -> x1]) -> false]]]]]; [(not false) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [(or x [x0 -> x1]) -> false]]]]].", + "intro.", + "c em", + "=> (em goal5).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em x).", + "c em", + "=> (em p1@type@2).", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 488, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "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 not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + 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(not 'P))] false))).", + "a x3", + "=> (and [x0 -> x1] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [(or x x0) -> (or x x1)] (and [('P : prop) -> (or 'P (not 'P))] false)))).", + "a exfalso", + "=> false.", + "a x3", + "=> (and (or x [x0 -> x1]) false).", + "a x3", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and (or x [x0 -> x1]) false)).", + "a and_i", + "=> (and (or x [x0 -> x1]) false).", + "a and_i", + "=> (or x [x0 -> x1]); false.", + "a x3", + "=> (and x0 (or x [x0 -> x1])).", + "a and_i", + "=> x0; (or x [x0 -> x1]).", + "a x3", + "=> (and (and [('P : prop) -> (or 'P (not 'P))] (and (or x [x0 -> x1]) false)) x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 397, + "actions": [ + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [x -> false]].", + "intro.", + "intro.", + "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]].", + "intro.", + "intro.", + "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)])].", + "a x4", + "=> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [('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].", + "c em", + "=> (em goal).", + "a x2", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x2", + "=> (iff (iff false [('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])]]).", + "a iff_i", + "=> [(iff false [('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])]]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "intro.", + "a x5", + "=> (iff [('C : prop) -> [[(or x7 'B) -> (or x7 'C)] -> (or x7 ['B -> 'C])]] 'B : prop).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_er@type).", + "c x4", + "=> (x4 false iff_er@type x6).", + "c x2", + "=> (x2 false iff_er@type x6).", + "c iff_er", + "=> (iff_er false iff_er@type x6).", + "c iff_el", + "=> (iff_el false iff_er@type x6).", + "c p5", + "=> (p5 x4).", + "c p4" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..c05ae4d8e40c2dcb29c46d7d3c36feb5c287e77e --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,846 @@ +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_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_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] - extrinsic_L0_5 (traces=2 evals=391) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] g extrinsic_L0_9 (traces=1 evals=321) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_5 (traces=1 evals=43) +[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 ] - extrinsic_L1_2 (traces=2 evals=426) +[OK ] - extrinsic_L1_1 (traces=2 evals=403) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] - extrinsic_L1_3 (traces=2 evals=426) +[OK ] g extrinsic_L2_12 (traces=1 evals=50) +[OK ] g extrinsic_L3_2 (traces=1 evals=33) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L3_4 (traces=3 evals=1059) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L3_5 (traces=3 evals=6801) +[OK ] - extrinsic_L3_1 (traces=8 evals=15726) + +thread '' (870471) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870471) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870471) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870471) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_12 (traces=17 evals=8485) +[ ] - extrinsic_L2_2 (traces=17 evals=20987) +[ ] - extrinsic_L3_9 (traces=17 evals=10026) +[ ] - extrinsic_L3_10 (traces=17 evals=13970) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[OK ] g extrinsic_L3_14 (traces=1 evals=170) +[OK ] - extrinsic_L3_12 (traces=8 evals=13030) +[ ] - extrinsic_L3_7 (traces=17 evals=18221) + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_13 (traces=17 evals=26352) +[OK ] - extrinsic_L3_18 (traces=7 evals=2576) +[ ] - extrinsic_L3_11 (traces=17 evals=20144) +[ ] - extrinsic_L3_8 (traces=17 evals=20972) +[OK ] - extrinsic_L3_17 (traces=7 evals=10577) +[ ] - extrinsic_L3_16 (traces=17 evals=18297) +[OK ] g extrinsic_L3_23 (traces=1 evals=59) +[ ] - extrinsic_L3_15 (traces=17 evals=26432) + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=17 evals=22300) + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_24 (traces=17 evals=27411) +[ ] - extrinsic_L3_21 (traces=17 evals=31698) +[ ] - extrinsic_L3_20 (traces=17 evals=29955) +[ ] - extrinsic_L3_22 (traces=15 evals=15791) +[OK ] - extrinsic_L3_25 (traces=17 evals=18849) + +thread '' (870472) 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=17 evals=20083) +[ ] - extrinsic_L4_1 (traces=17 evals=18591) +[ ] - extrinsic_L3_26 (traces=15 evals=12471) +[ ] - extrinsic_L4_2 (traces=17 evals=21969) +[ ] - extrinsic_L3_29 (traces=15 evals=14715) +[ ] - extrinsic_L3_28 (traces=12 evals=19267) +[ ] - extrinsic_L4_3 (traces=17 evals=21684) + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_4 (traces=7 evals=17926) +[ ] - extrinsic_L4_5 (traces=17 evals=20323) +[ ] - extrinsic_L4_6 (traces=10 evals=21709) +[ ] - extrinsic_L4_7 (traces=17 evals=32244) +[ ] - extrinsic_L4_8 (traces=17 evals=15115) +[ ] - extrinsic_L4_9 (traces=17 evals=33194) +[ ] - extrinsic_L4_10 (traces=15 evals=24765) +[ ] - extrinsic_L4_11 (traces=17 evals=33531) + +thread '' (870466) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L4_14 (traces=17 evals=33207) +[ ] - extrinsic_L4_13 (traces=14 evals=29201) +[ ] - extrinsic_L4_12 (traces=15 evals=31156) +[ ] - extrinsic_L5_2 (traces=17 evals=11658) +[ ] - extrinsic_L5_1 (traces=17 evals=22452) +[ ] - extrinsic_L5_3 (traces=17 evals=28888) +[ ] - extrinsic_L5_6 (traces=17 evals=13180) + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870469) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_5 (traces=17 evals=26462) + +thread '' (870466) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870466) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=17 evals=23454) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) + +thread '' (870472) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870472) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=11 evals=28581) +[ ] - extrinsic_L5_9 (traces=17 evals=9987) + +thread '' (870471) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_11 (traces=17 evals=13632) +[ ] - extrinsic_L5_7 (traces=15 evals=21576) +[OK ] g extrinsic_L6_6 (traces=1 evals=54) + +thread '' (870466) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (870466) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_10 (traces=9 evals=26827) +[ ] - extrinsic_L6_5 (traces=17 evals=16708) + +thread '' (870466) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_2 (traces=16 evals=13805) +[ ] - extrinsic_L6_8 (traces=17 evals=8599) +[ ] - extrinsic_L6_9 (traces=17 evals=18883) +[ ] - extrinsic_L6_7 (traces=10 evals=12163) +[ ] - extrinsic_L6_3 (traces=6 evals=131191) +[ ] - extrinsic_L6_4 (traces=7 evals=153936) +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/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 43/94 in 4546.6s diff --git a/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_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/s46/2026-06-28_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/s46/train.log b/experiments/learnability/train_policy_only/minimo_1pt/s46/train.log new file mode 100644 index 0000000000000000000000000000000000000000..dcf5e1f909800093e8a787d7080fba1297a6301c --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_1pt/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_053114-zkkv90bk +[2026-06-28T05:31:10.278149] Seeded RNGs with seed=46 +[2026-06-28T05:31:10.278369] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-28T05:31:13.853456] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_1pt/examples_policy_only.json + 1880 training examples loaded. + +============================================================ +[2026-06-28T05:31:13.855975] 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/s46/2026-06-28_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/s46/2026-06-28_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/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 60 total steps, 1880 unique examples (batch_size=64) +[2026-06-28T05:31:26.913533] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:31:26.922572] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_1pt/s46/2026-06-28_05-31-10/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 60} diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..5ee3c44e5f709b0b8f2672fb8b0d7252659bd91f --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/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_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_2.pt", + "problemset": "extrinsic-95", + "max_pops": 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"extrinsic_L5_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26970, + "max_open": 22971, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31099, + "max_open": 27100, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25733, + "max_open": 21734, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31038, + "max_open": 27039, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31003, + "max_open": 27004, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30901, + "max_open": 26902, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30830, + "max_open": 26831, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25982, + "max_open": 21983, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25795, + "max_open": 21796, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31281, + "max_open": 27282, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26080, + "max_open": 22081, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..50d83596b5129e6867fa723cfcd0682c663a4769 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/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=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_2 (solved pops=49 evals=312 maxopen=264) +[OK ] extrinsic_L0_3 (solved pops=58 evals=381 maxopen=324) +[OK ] extrinsic_L0_5 (solved pops=51 evals=317 maxopen=267) +[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_8 (solved pops=55 evals=355 maxopen=301) +[OK ] extrinsic_L0_7 (solved pops=59 evals=382 maxopen=324) +[OK ] extrinsic_L0_12 (solved pops=12 evals=82 maxopen=54) +[OK ] extrinsic_L0_13 (solved pops=25 evals=176 maxopen=152) +[OK ] extrinsic_L0_9 (solved pops=47 evals=324 maxopen=262) +[OK ] extrinsic_L0_4 (solved pops=216 evals=1136 maxopen=921) +[OK ] extrinsic_L1_4 (solved pops=17 evals=132 maxopen=114) +[OK ] extrinsic_L0_11 (solved pops=215 evals=1155 maxopen=941) +[OK ] extrinsic_L1_1 (solved pops=231 evals=1254 maxopen=1006) +[OK ] extrinsic_L1_3 (solved pops=503 evals=2685 maxopen=2183) +[OK ] extrinsic_L1_2 (solved pops=503 evals=2688 maxopen=2186) +[OK ] extrinsic_L2_1 (solved pops=1147 evals=6483 maxopen=5337) +[OK ] extrinsic_L2_6 (solved pops=1785 evals=10445 maxopen=8661) +[OK ] extrinsic_L2_7 (solved pops=892 evals=4960 maxopen=4069) +[OK ] extrinsic_L0_14 (solved pops=3764 evals=24735 maxopen=20972) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25897 maxopen=21898) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25965 maxopen=21966) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25960 maxopen=21961) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25714 maxopen=21715) +[OK ] extrinsic_L2_9 (solved pops=943 evals=5248 maxopen=4306) +[OK ] extrinsic_L2_12 (solved pops=1163 evals=6555 maxopen=5393) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26502 maxopen=22503) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26133 maxopen=22134) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25639 maxopen=21640) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25963 maxopen=21964) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25674 maxopen=21675) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25710 maxopen=21711) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25984 maxopen=21985) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25973 maxopen=21974) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25715 maxopen=21716) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25903 maxopen=21904) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25965 maxopen=21966) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26130 maxopen=22131) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25964 maxopen=21965) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25802 maxopen=21803) +[OK ] extrinsic_L3_14 (solved pops=3379 evals=21651 maxopen=18273) +[OK ] extrinsic_L3_13 (solved pops=3421 evals=22511 maxopen=19091) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25788 maxopen=21789) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26020 maxopen=22021) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26018 maxopen=22019) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25901 maxopen=21902) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25385 maxopen=21386) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26104 maxopen=22105) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26197 maxopen=22198) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26000 maxopen=22001) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25845 maxopen=21846) +[ ] extrinsic_L3_23 (budget pops=4000 evals=25962 maxopen=21963) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26476 maxopen=22477) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27245 maxopen=23246) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26148 maxopen=22149) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26247 maxopen=22248) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26095 maxopen=22096) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26279 maxopen=22280) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26886 maxopen=22887) +[ ] extrinsic_L4_2 (budget pops=4000 evals=27107 maxopen=23108) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26043 maxopen=22044) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25846 maxopen=21847) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26095 maxopen=22096) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25876 maxopen=21877) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26643 maxopen=22644) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26408 maxopen=22409) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26026 maxopen=22027) +[OK ] extrinsic_L4_12 (solved pops=1299 evals=7458 maxopen=6157) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25857 maxopen=21858) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26564 maxopen=22565) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25860 maxopen=21861) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26215 maxopen=22216) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25883 maxopen=21884) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26205 maxopen=22206) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26265 maxopen=22266) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25747 maxopen=21748) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26206 maxopen=22207) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26448 maxopen=22449) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26358 maxopen=22359) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26307 maxopen=22308) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26336 maxopen=22337) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26970 maxopen=22971) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25733 maxopen=21734) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31099 maxopen=27100) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31038 maxopen=27039) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31003 maxopen=27004) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30901 maxopen=26902) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30830 maxopen=26831) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25795 maxopen=21796) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25982 maxopen=21983) +[ ] extrinsic_L6_9 (budget pops=4000 evals=26080 maxopen=22081) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31281 maxopen=27282) +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 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"extrinsic_L4_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26489, + "max_open": 22490, + "solution_actions": null, + "problem": "extrinsic_L4_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25593, + "max_open": 21594, + "solution_actions": null, + "problem": "extrinsic_L4_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26398, + "max_open": 22399, + "solution_actions": null, + "problem": "extrinsic_L4_11" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 1355, + "evals_used": 7618, + "max_open": 6261, + "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": 26049, + "max_open": 22050, + "solution_actions": null, + "problem": "extrinsic_L4_13" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26324, + "max_open": 22325, + "solution_actions": null, + "problem": "extrinsic_L4_14" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26490, + "max_open": 22491, + "solution_actions": null, + "problem": "extrinsic_L5_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26196, + "max_open": 22197, + "solution_actions": null, + "problem": "extrinsic_L5_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26242, + "max_open": 22243, + "solution_actions": null, + "problem": "extrinsic_L5_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26464, + "max_open": 22465, + "solution_actions": null, + "problem": "extrinsic_L5_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26439, + "max_open": 22440, + "solution_actions": null, + 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"max_open": 27077, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26108, + "max_open": 22109, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31118, + "max_open": 27119, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31054, + "max_open": 27055, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30951, + "max_open": 26952, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31100, + "max_open": 27101, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25910, + "max_open": 21911, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26007, + "max_open": 22008, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31285, + "max_open": 27286, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31150, + "max_open": 27151, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..b9ab0b1f5f88b24bb80130d85bda458890999535 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/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=53 evals=346 maxopen=294) +[OK ] extrinsic_L0_6 (solved pops=51 evals=342 maxopen=292) +[OK ] extrinsic_L0_5 (solved pops=55 evals=349 maxopen=295) +[OK ] extrinsic_L0_3 (solved pops=58 evals=376 maxopen=319) +[OK ] extrinsic_L0_7 (solved pops=57 evals=358 maxopen=302) +[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_13 (solved pops=25 evals=176 maxopen=152) +[OK ] extrinsic_L0_9 (solved pops=51 evals=358 maxopen=292) +[OK ] extrinsic_L0_8 (solved pops=55 evals=353 maxopen=299) +[OK ] extrinsic_L0_4 (solved pops=199 evals=1060 maxopen=862) +[OK ] extrinsic_L1_4 (solved pops=18 evals=120 maxopen=101) +[OK ] extrinsic_L0_11 (solved pops=205 evals=1107 maxopen=903) +[OK ] extrinsic_L1_1 (solved pops=235 evals=1257 maxopen=1005) +[OK ] extrinsic_L1_2 (solved pops=399 evals=2071 maxopen=1673) +[OK ] extrinsic_L1_3 (solved pops=399 evals=2068 maxopen=1670) +[OK ] extrinsic_L2_1 (solved pops=1286 evals=7131 maxopen=5846) +[OK ] extrinsic_L2_6 (solved pops=1594 evals=9075 maxopen=7482) +[OK ] extrinsic_L2_7 (solved pops=987 evals=5590 maxopen=4604) +[ ] extrinsic_L0_14 (budget pops=4000 evals=26336 maxopen=22337) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26177 maxopen=22178) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25915 maxopen=21916) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25910 maxopen=21911) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25775 maxopen=21776) +[OK ] extrinsic_L2_9 (solved pops=916 evals=5153 maxopen=4238) +[OK ] extrinsic_L2_12 (solved pops=1297 evals=7200 maxopen=5904) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26395 maxopen=22396) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26260 maxopen=22261) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25703 maxopen=21704) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25946 maxopen=21947) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25747 maxopen=21748) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25778 maxopen=21779) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26054 maxopen=22055) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26059 maxopen=22060) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25777 maxopen=21778) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25948 maxopen=21949) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26111 maxopen=22112) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26212 maxopen=22213) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26073 maxopen=22074) +[OK ] extrinsic_L3_13 (solved pops=3121 evals=18776 maxopen=15656) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25817 maxopen=21818) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25822 maxopen=21823) +[OK ] extrinsic_L3_14 (solved pops=3315 evals=21523 maxopen=18209) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26249 maxopen=22250) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26219 maxopen=22220) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25913 maxopen=21914) +[ ] extrinsic_L3_18 (budget pops=4000 evals=26011 maxopen=22012) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25960 maxopen=21961) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26089 maxopen=22090) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26124 maxopen=22125) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25967 maxopen=21968) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26285 maxopen=22286) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26204 maxopen=22205) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26933 maxopen=22934) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26075 maxopen=22076) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26094 maxopen=22095) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26089 maxopen=22090) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26659 maxopen=22660) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26895 maxopen=22896) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26042 maxopen=22043) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26830 maxopen=22831) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25961 maxopen=21962) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25960 maxopen=21961) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26143 maxopen=22144) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26882 maxopen=22883) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26489 maxopen=22490) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26176 maxopen=22177) +[OK ] extrinsic_L4_12 (solved pops=1355 evals=7618 maxopen=6261) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25593 maxopen=21594) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26398 maxopen=22399) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26049 maxopen=22050) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26324 maxopen=22325) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26490 maxopen=22491) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26196 maxopen=22197) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26242 maxopen=22243) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26464 maxopen=22465) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26299 maxopen=22300) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26439 maxopen=22440) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26392 maxopen=22393) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26393 maxopen=22394) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26610 maxopen=22611) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26764 maxopen=22765) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26108 maxopen=22109) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31076 maxopen=27077) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31118 maxopen=27119) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30951 maxopen=26952) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31054 maxopen=27055) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31100 maxopen=27101) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25910 maxopen=21911) +[ ] extrinsic_L6_7 (budget pops=4000 evals=26007 maxopen=22008) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31285 maxopen=27286) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31150 maxopen=27151) +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 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('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=48 evals=296 maxopen=249) +[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_3 (solved pops=62 evals=396 maxopen=335) +[OK ] extrinsic_L0_7 (solved pops=62 evals=380 maxopen=319) +[OK ] extrinsic_L0_12 (solved pops=10 evals=78 maxopen=52) +[OK ] extrinsic_L0_13 (solved pops=24 evals=176 maxopen=153) +[OK ] extrinsic_L0_9 (solved pops=46 evals=308 maxopen=247) +[OK ] extrinsic_L0_8 (solved pops=58 evals=368 maxopen=311) +[OK ] extrinsic_L0_4 (solved pops=221 evals=1190 maxopen=970) +[OK ] extrinsic_L1_4 (solved pops=15 evals=101 maxopen=85) +[OK ] extrinsic_L0_11 (solved pops=220 evals=1179 maxopen=960) +[OK ] extrinsic_L1_1 (solved pops=238 evals=1269 maxopen=1014) +[OK ] extrinsic_L1_2 (solved pops=505 evals=2692 maxopen=2188) +[OK ] extrinsic_L1_3 (solved pops=505 evals=2689 maxopen=2185) +[OK ] extrinsic_L2_1 (solved pops=1178 evals=6730 maxopen=5553) +[OK ] extrinsic_L2_6 (solved pops=1844 evals=10835 maxopen=8992) +[OK ] extrinsic_L2_7 (solved pops=876 evals=4906 maxopen=4031) +[OK ] extrinsic_L0_14 (solved pops=3736 evals=24541 maxopen=20806) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25963 maxopen=21964) +[ ] extrinsic_L2_3 (budget pops=4000 evals=26049 maxopen=22050) +[OK ] extrinsic_L2_11 (solved pops=26 evals=181 maxopen=154) +[ ] extrinsic_L2_4 (budget pops=4000 evals=26044 maxopen=22045) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25725 maxopen=21726) +[OK ] extrinsic_L2_9 (solved pops=937 evals=5261 maxopen=4325) +[OK ] extrinsic_L2_12 (solved pops=1138 evals=6494 maxopen=5357) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26646 maxopen=22647) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26127 maxopen=22128) +[ ] extrinsic_L3_1 (budget pops=4000 evals=26047 maxopen=22048) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25683 maxopen=21684) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25665 maxopen=21666) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25722 maxopen=21723) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25990 maxopen=21991) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25979 maxopen=21980) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25726 maxopen=21727) +[ ] extrinsic_L3_7 (budget pops=4000 evals=26008 maxopen=22009) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26084 maxopen=22085) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26203 maxopen=22204) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26039 maxopen=22040) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25793 maxopen=21794) +[OK ] extrinsic_L3_13 (solved pops=3496 evals=23307 maxopen=19812) +[OK ] extrinsic_L3_14 (solved pops=3392 evals=22071 maxopen=18680) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25809 maxopen=21810) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26088 maxopen=22089) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26031 maxopen=22032) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25965 maxopen=21966) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25114 maxopen=21115) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26264 maxopen=22265) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26186 maxopen=22187) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25982 maxopen=21983) +[ ] extrinsic_L3_22 (budget pops=4000 evals=26013 maxopen=22014) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26001 maxopen=22002) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26451 maxopen=22452) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27252 maxopen=23253) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26271 maxopen=22272) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26283 maxopen=22284) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26083 maxopen=22084) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26342 maxopen=22343) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26873 maxopen=22874) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26050 maxopen=22051) +[ ] extrinsic_L4_2 (budget pops=4000 evals=27093 maxopen=23094) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25890 maxopen=21891) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26231 maxopen=22232) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25891 maxopen=21892) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26688 maxopen=22689) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26422 maxopen=22423) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25971 maxopen=21972) +[OK ] extrinsic_L4_12 (solved pops=1260 evals=7291 maxopen=6029) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25849 maxopen=21850) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26536 maxopen=22537) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25550 maxopen=21551) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26291 maxopen=22292) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25586 maxopen=21587) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26266 maxopen=22267) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26321 maxopen=22322) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25500 maxopen=21501) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26468 maxopen=22469) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26183 maxopen=22184) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26401 maxopen=22402) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26428 maxopen=22429) +[ ] extrinsic_L5_9 (budget pops=4000 evals=25846 maxopen=21847) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31177 maxopen=27178) +[ ] extrinsic_L5_10 (budget pops=4000 evals=27051 maxopen=23052) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25770 maxopen=21771) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31111 maxopen=27112) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30956 maxopen=26957) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31120 maxopen=27121) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30879 maxopen=26880) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25872 maxopen=21873) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25940 maxopen=21941) +[ ] extrinsic_L6_9 (budget pops=4000 evals=26018 maxopen=22019) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31206 maxopen=27207) +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) -> 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27131, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..d60160d8d5e4d99057ccb696c372b7be914cb13c --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/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_3 (solved pops=59 evals=380 maxopen=322) +[OK ] extrinsic_L0_2 (solved pops=50 evals=327 maxopen=278) +[OK ] extrinsic_L0_5 (solved pops=56 evals=367 maxopen=312) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_6 (solved pops=53 evals=346 maxopen=294) +[OK ] extrinsic_L0_8 (solved pops=54 evals=350 maxopen=297) +[OK ] extrinsic_L0_9 (solved pops=51 evals=358 maxopen=292) +[OK ] extrinsic_L0_7 (solved pops=57 evals=358 maxopen=302) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=23 evals=172 maxopen=150) +[OK ] extrinsic_L0_4 (solved pops=202 evals=1081 maxopen=880) +[OK ] extrinsic_L1_4 (solved pops=16 evals=116 maxopen=99) +[OK ] extrinsic_L0_11 (solved pops=204 evals=1091 maxopen=888) +[OK ] extrinsic_L1_1 (solved pops=246 evals=1323 maxopen=1060) +[OK ] extrinsic_L1_2 (solved pops=400 evals=2056 maxopen=1657) +[OK ] extrinsic_L1_3 (solved pops=400 evals=2053 maxopen=1654) +[OK ] extrinsic_L2_1 (solved pops=1299 evals=7202 maxopen=5904) +[OK ] extrinsic_L2_6 (solved pops=1622 evals=9332 maxopen=7711) +[OK ] extrinsic_L2_7 (solved pops=990 evals=5611 maxopen=4622) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26106 maxopen=22107) +[ ] extrinsic_L0_14 (budget pops=4000 evals=26339 maxopen=22340) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25984 maxopen=21985) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25979 maxopen=21980) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25772 maxopen=21773) +[OK ] extrinsic_L2_9 (solved pops=933 evals=5275 maxopen=4343) +[OK ] extrinsic_L2_12 (solved pops=1313 evals=7291 maxopen=5979) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26372 maxopen=22373) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26215 maxopen=22216) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25730 maxopen=21731) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25982 maxopen=21983) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25802 maxopen=21803) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25815 maxopen=21816) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25989 maxopen=21990) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25963 maxopen=21964) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25773 maxopen=21774) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25966 maxopen=21967) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25992 maxopen=21993) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26201 maxopen=22202) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25978 maxopen=21979) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25743 maxopen=21744) +[OK ] extrinsic_L3_13 (solved pops=3169 evals=19505 maxopen=16337) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25743 maxopen=21744) +[OK ] extrinsic_L3_14 (solved pops=3354 evals=21794 maxopen=18441) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26169 maxopen=22170) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26158 maxopen=22159) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25856 maxopen=21857) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25884 maxopen=21885) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25899 maxopen=21900) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26025 maxopen=22026) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26130 maxopen=22131) +[ ] extrinsic_L3_22 (budget pops=4000 evals=26008 maxopen=22009) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26418 maxopen=22419) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26142 maxopen=22143) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26068 maxopen=22069) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26961 maxopen=22962) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26050 maxopen=22051) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26123 maxopen=22124) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26642 maxopen=22643) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26850 maxopen=22851) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26036 maxopen=22037) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26867 maxopen=22868) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25885 maxopen=21886) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25887 maxopen=21888) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26078 maxopen=22079) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26899 maxopen=22900) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26428 maxopen=22429) +[ ] extrinsic_L4_8 (budget pops=4000 evals=25935 maxopen=21936) +[OK ] extrinsic_L4_12 (solved pops=1315 evals=7458 maxopen=6141) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25759 maxopen=21760) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26332 maxopen=22333) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25993 maxopen=21994) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26172 maxopen=22173) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26395 maxopen=22396) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26229 maxopen=22230) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26191 maxopen=22192) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26342 maxopen=22343) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26168 maxopen=22169) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26441 maxopen=22442) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26376 maxopen=22377) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26333 maxopen=22334) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26597 maxopen=22598) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26772 maxopen=22773) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26112 maxopen=22113) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31051 maxopen=27052) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31087 maxopen=27088) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30886 maxopen=26887) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31049 maxopen=27050) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31174 maxopen=27175) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25884 maxopen=21885) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26092 maxopen=22093) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31141 maxopen=27142) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31130 maxopen=27131) +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) -> 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'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_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 26/94 in 2740.0s diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0fd959bb42bece230d26a6e3daaefd4c1bb618 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/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_gold/gold_0pt/s44/2026-06-29_07-09-16/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, + "num_solved": 27, + "elapsed_sec": 2742.5606315135956, + "results": [ + { + "solved": true, + 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b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..78e338bc71a3c99d788842d4f69c7bfab0e340eb --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/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=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_2 (solved pops=49 evals=312 maxopen=264) +[OK ] extrinsic_L0_5 (solved pops=51 evals=317 maxopen=267) +[OK ] extrinsic_L0_3 (solved pops=61 evals=393 maxopen=333) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_6 (solved pops=49 evals=312 maxopen=264) +[OK ] extrinsic_L0_12 (solved pops=10 evals=78 maxopen=52) +[OK ] extrinsic_L0_7 (solved pops=70 evals=419 maxopen=350) +[OK ] extrinsic_L0_8 (solved pops=67 evals=411 maxopen=345) +[OK ] extrinsic_L0_13 (solved pops=26 evals=180 maxopen=155) +[OK ] extrinsic_L0_9 (solved pops=46 evals=308 maxopen=247) +[OK ] extrinsic_L0_4 (solved pops=208 evals=1092 maxopen=885) +[OK ] extrinsic_L1_4 (solved pops=15 evals=101 maxopen=85) +[OK ] extrinsic_L0_11 (solved pops=213 evals=1151 maxopen=939) +[OK ] extrinsic_L1_1 (solved pops=234 evals=1273 maxopen=1022) +[OK ] extrinsic_L1_2 (solved pops=509 evals=2730 maxopen=2222) +[OK ] extrinsic_L1_3 (solved pops=509 evals=2727 maxopen=2219) +[OK ] extrinsic_L2_1 (solved pops=1229 evals=6876 maxopen=5648) +[OK ] extrinsic_L2_6 (solved pops=1735 evals=10127 maxopen=8393) +[OK ] extrinsic_L2_7 (solved pops=951 evals=5360 maxopen=4410) +[OK ] extrinsic_L0_14 (solved pops=3765 evals=24727 maxopen=20963) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26068 maxopen=22069) +[ ] extrinsic_L2_3 (budget pops=4000 evals=26011 maxopen=22012) +[OK ] extrinsic_L2_11 (solved pops=26 evals=181 maxopen=154) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25994 maxopen=21995) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25777 maxopen=21778) +[OK ] extrinsic_L2_9 (solved pops=939 evals=5265 maxopen=4327) +[OK ] extrinsic_L2_12 (solved pops=1162 evals=6553 maxopen=5392) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26693 maxopen=22694) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26153 maxopen=22154) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25690 maxopen=21691) +[ ] extrinsic_L3_1 (budget pops=4000 evals=26011 maxopen=22012) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25743 maxopen=21744) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25749 maxopen=21750) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25983 maxopen=21984) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25988 maxopen=21989) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25779 maxopen=21780) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25950 maxopen=21951) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26091 maxopen=22092) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26200 maxopen=22201) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26076 maxopen=22077) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25808 maxopen=21809) +[OK ] extrinsic_L3_13 (solved pops=3480 evals=23139 maxopen=19660) +[OK ] extrinsic_L3_14 (solved pops=3387 evals=22538 maxopen=19152) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25825 maxopen=21826) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26051 maxopen=22052) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26056 maxopen=22057) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25899 maxopen=21900) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25353 maxopen=21354) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26255 maxopen=22256) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26156 maxopen=22157) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25999 maxopen=22000) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25903 maxopen=21904) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26080 maxopen=22081) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26427 maxopen=22428) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26171 maxopen=22172) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27310 maxopen=23311) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26262 maxopen=22263) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26094 maxopen=22095) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26341 maxopen=22342) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26889 maxopen=22890) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26101 maxopen=22102) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26989 maxopen=22990) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25923 maxopen=21924) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26156 maxopen=22157) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25956 maxopen=21957) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26709 maxopen=22710) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26040 maxopen=22041) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26347 maxopen=22348) +[OK ] extrinsic_L4_12 (solved pops=1238 evals=7140 maxopen=5900) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25908 maxopen=21909) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26631 maxopen=22632) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25802 maxopen=21803) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26289 maxopen=22290) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25788 maxopen=21789) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26242 maxopen=22243) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26295 maxopen=22296) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25663 maxopen=21664) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26450 maxopen=22451) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26222 maxopen=22223) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26481 maxopen=22482) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26367 maxopen=22368) +[ ] extrinsic_L5_9 (budget pops=4000 evals=25889 maxopen=21890) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26833 maxopen=22834) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25770 maxopen=21771) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31121 maxopen=27122) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31080 maxopen=27081) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31078 maxopen=27079) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30871 maxopen=26872) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30838 maxopen=26839) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25878 maxopen=21879) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25943 maxopen=21944) +[ ] extrinsic_L6_9 (budget pops=4000 evals=26140 maxopen=22141) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31249 maxopen=27250) +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]] 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[(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_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json +Solved 27/94 in 2742.6s diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json new file mode 100644 index 0000000000000000000000000000000000000000..e2de4b5b7843f52c312824a9ba5511ac68b0f42b --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json @@ -0,0 +1,1048 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_1.pt", + "problemset": "extrinsic-95", + "max_pops": 4000, + "max_actions": 0, + "timeout": 600.0, + "workers": 6, + "num_problems": 94, + "num_solved": 26, + "elapsed_sec": 2770.471202850342, + "results": [ + { + "solved": true, + "outcome": "solved", + "pops_used": 3, + "evals_used": 21, + "max_open": 17, + "solution_actions": [ + "intro.", + "intro." + ], + "problem": "extrinsic_L0_1" + }, + { + "solved": 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4000, + "evals_used": 25987, + "max_open": 21988, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31451, + "max_open": 27452, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31144, + "max_open": 27145, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..d453f3cf3b4150e6e0b2f8738536dc3f510bb1f2 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/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=53 evals=346 maxopen=294) +[OK ] extrinsic_L0_3 (solved pops=57 evals=373 maxopen=317) +[OK ] extrinsic_L0_5 (solved pops=58 evals=371 maxopen=314) +[OK ] extrinsic_L0_6 (solved pops=51 evals=342 maxopen=292) +[OK ] extrinsic_L0_10 (solved pops=7 evals=41 maxopen=35) +[OK ] extrinsic_L0_7 (solved pops=57 evals=358 maxopen=302) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_8 (solved pops=55 evals=353 maxopen=299) +[OK ] extrinsic_L0_13 (solved pops=21 evals=167 maxopen=147) +[OK ] extrinsic_L0_9 (solved pops=53 evals=362 maxopen=294) +[OK ] extrinsic_L0_4 (solved pops=201 evals=1064 maxopen=864) +[OK ] extrinsic_L1_4 (solved pops=16 evals=116 maxopen=99) +[OK ] extrinsic_L0_11 (solved pops=205 evals=1107 maxopen=903) +[OK ] extrinsic_L1_1 (solved pops=228 evals=1229 maxopen=984) +[OK ] extrinsic_L1_2 (solved pops=386 evals=1967 maxopen=1582) +[OK ] extrinsic_L1_3 (solved pops=386 evals=1964 maxopen=1579) +[OK ] extrinsic_L2_1 (solved pops=1288 evals=7152 maxopen=5865) +[OK ] extrinsic_L2_6 (solved pops=1564 evals=8945 maxopen=7382) +[OK ] extrinsic_L2_7 (solved pops=984 evals=5582 maxopen=4599) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26247 maxopen=22248) +[ ] extrinsic_L0_14 (budget pops=4000 evals=26335 maxopen=22336) +[ ] extrinsic_L2_3 (budget pops=4000 evals=26018 maxopen=22019) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=26013 maxopen=22014) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25831 maxopen=21832) +[OK ] extrinsic_L2_9 (solved pops=939 evals=5287 maxopen=4349) +[OK ] extrinsic_L2_12 (solved pops=1295 evals=7228 maxopen=5934) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26255 maxopen=22256) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26299 maxopen=22300) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25737 maxopen=21738) +[ ] extrinsic_L3_1 (budget pops=4000 evals=26034 maxopen=22035) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25781 maxopen=21782) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25802 maxopen=21803) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26051 maxopen=22052) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26040 maxopen=22041) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25849 maxopen=21850) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25957 maxopen=21958) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26197 maxopen=22198) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26235 maxopen=22236) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26127 maxopen=22128) +[OK ] extrinsic_L3_13 (solved pops=3157 evals=18850 maxopen=15694) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25875 maxopen=21876) +[OK ] extrinsic_L3_14 (solved pops=3305 evals=20868 maxopen=17564) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25899 maxopen=21900) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26275 maxopen=22276) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26244 maxopen=22245) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25900 maxopen=21901) +[ ] extrinsic_L3_18 (budget pops=4000 evals=26064 maxopen=22065) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26001 maxopen=22002) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26130 maxopen=22131) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26145 maxopen=22146) +[ ] extrinsic_L3_22 (budget pops=4000 evals=26049 maxopen=22050) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26307 maxopen=22308) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26264 maxopen=22265) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26076 maxopen=22077) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26993 maxopen=22994) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26145 maxopen=22146) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26139 maxopen=22140) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26589 maxopen=22590) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26903 maxopen=22904) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26019 maxopen=22020) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26311 maxopen=22312) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25968 maxopen=21969) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26165 maxopen=22166) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25957 maxopen=21958) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26892 maxopen=22893) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26205 maxopen=22206) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26511 maxopen=22512) +[OK ] extrinsic_L4_12 (solved pops=1335 evals=7524 maxopen=6187) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25618 maxopen=21619) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26329 maxopen=22330) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26110 maxopen=22111) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26370 maxopen=22371) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26567 maxopen=22568) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26264 maxopen=22265) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26336 maxopen=22337) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26504 maxopen=22505) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26483 maxopen=22484) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26245 maxopen=22246) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26439 maxopen=22440) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26429 maxopen=22430) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26609 maxopen=22610) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26837 maxopen=22838) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31185 maxopen=27186) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26136 maxopen=22137) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31134 maxopen=27135) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31072 maxopen=27073) +[ ] extrinsic_L6_4 (budget pops=4000 evals=31042 maxopen=27043) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31091 maxopen=27092) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26116 maxopen=22117) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25987 maxopen=21988) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31451 maxopen=27452) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31144 maxopen=27145) +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 : 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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 : 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('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 : 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-> ('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_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 26/94 in 2770.5s diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..dbeff2900aa2c82582cec794d5e29f705464b203 --- /dev/null +++ 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null, + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26302, + "max_open": 22303, + "solution_actions": null, + "problem": "extrinsic_L5_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26377, + "max_open": 22378, + "solution_actions": null, + "problem": "extrinsic_L5_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26825, + "max_open": 22826, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31132, + "max_open": 27133, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25810, + "max_open": 21811, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31069, + "max_open": 27070, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31033, + "max_open": 27034, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30894, + "max_open": 26895, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30903, + "max_open": 26904, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25922, + "max_open": 21923, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25829, + "max_open": 21830, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31200, + "max_open": 27201, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26105, + "max_open": 22106, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..75bbd8eafe4184cedce082cfc789265e1d5a38d8 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/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=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_2 (solved pops=49 evals=312 maxopen=264) +[OK ] extrinsic_L0_6 (solved pops=50 evals=327 maxopen=278) +[OK ] extrinsic_L0_5 (solved pops=52 evals=332 maxopen=281) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_3 (solved pops=61 evals=393 maxopen=333) +[OK ] extrinsic_L0_12 (solved pops=10 evals=78 maxopen=52) +[OK ] extrinsic_L0_7 (solved pops=73 evals=429 maxopen=357) +[OK ] extrinsic_L0_13 (solved pops=25 evals=176 maxopen=152) +[OK ] extrinsic_L0_9 (solved pops=47 evals=324 maxopen=262) +[OK ] extrinsic_L0_8 (solved pops=69 evals=417 maxopen=349) +[OK ] extrinsic_L0_4 (solved pops=208 evals=1092 maxopen=885) +[OK ] extrinsic_L1_4 (solved pops=16 evals=117 maxopen=100) +[OK ] extrinsic_L0_11 (solved pops=211 evals=1119 maxopen=909) +[OK ] extrinsic_L1_1 (solved pops=230 evals=1238 maxopen=991) +[OK ] extrinsic_L1_2 (solved pops=512 evals=2781 maxopen=2270) +[OK ] extrinsic_L1_3 (solved pops=512 evals=2778 maxopen=2267) +[OK ] extrinsic_L2_1 (solved pops=1190 evals=6650 maxopen=5461) +[OK ] extrinsic_L2_6 (solved pops=1677 evals=9653 maxopen=7977) +[OK ] extrinsic_L2_7 (solved pops=932 evals=5232 maxopen=4301) +[OK ] extrinsic_L0_14 (solved pops=3875 evals=25458 maxopen=21584) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25975 maxopen=21976) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25987 maxopen=21988) +[OK ] extrinsic_L2_11 (solved pops=26 evals=181 maxopen=154) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25978 maxopen=21979) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25705 maxopen=21706) +[OK ] extrinsic_L2_9 (solved pops=937 evals=5236 maxopen=4300) +[OK ] extrinsic_L2_12 (solved pops=1179 evals=6615 maxopen=5437) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26554 maxopen=22555) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26064 maxopen=22065) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25717 maxopen=21718) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25985 maxopen=21986) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25731 maxopen=21732) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25766 maxopen=21767) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26001 maxopen=22002) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25993 maxopen=21994) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25706 maxopen=21707) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25979 maxopen=21980) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26056 maxopen=22057) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26180 maxopen=22181) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26066 maxopen=22067) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25711 maxopen=21712) +[OK ] extrinsic_L3_13 (solved pops=3430 evals=22589 maxopen=19160) +[OK ] extrinsic_L3_14 (solved pops=3373 evals=21839 maxopen=18467) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25716 maxopen=21717) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26045 maxopen=22046) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26053 maxopen=22054) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25872 maxopen=21873) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25585 maxopen=21586) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26135 maxopen=22136) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26212 maxopen=22213) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26009 maxopen=22010) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25920 maxopen=21921) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26057 maxopen=22058) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26431 maxopen=22432) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27293 maxopen=23294) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26107 maxopen=22108) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26249 maxopen=22250) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26093 maxopen=22094) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26318 maxopen=22319) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26916 maxopen=22917) +[ ] extrinsic_L4_2 (budget pops=4000 evals=27009 maxopen=23010) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26108 maxopen=22109) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25935 maxopen=21936) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26152 maxopen=22153) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25939 maxopen=21940) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26623 maxopen=22624) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26335 maxopen=22336) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26000 maxopen=22001) +[OK ] extrinsic_L4_12 (solved pops=1266 evals=7304 maxopen=6036) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25862 maxopen=21863) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26630 maxopen=22631) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25831 maxopen=21832) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26343 maxopen=22344) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26330 maxopen=22331) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26188 maxopen=22189) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26248 maxopen=22249) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26223 maxopen=22224) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26437 maxopen=22438) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26242 maxopen=22243) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26372 maxopen=22373) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26302 maxopen=22303) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26377 maxopen=22378) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26825 maxopen=22826) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31132 maxopen=27133) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25810 maxopen=21811) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31069 maxopen=27070) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31033 maxopen=27034) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30894 maxopen=26895) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30903 maxopen=26904) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25829 maxopen=21830) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25922 maxopen=21923) +[ ] extrinsic_L6_9 (budget pops=4000 evals=26105 maxopen=22106) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31200 maxopen=27201) +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] 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false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26793, + "max_open": 22794, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31150, + "max_open": 27151, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26145, + "max_open": 22146, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31131, + "max_open": 27132, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31113, + "max_open": 27114, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30997, + "max_open": 26998, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31065, + "max_open": 27066, + "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": 26000, + "max_open": 22001, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31296, + "max_open": 27297, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31119, + "max_open": 27120, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..8e622a12b4f895eb7f6f6bf529e9e27fe3a5b87f --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/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=58 evals=371 maxopen=314) +[OK ] extrinsic_L0_2 (solved pops=53 evals=346 maxopen=294) +[OK ] extrinsic_L0_6 (solved pops=51 evals=342 maxopen=292) +[OK ] extrinsic_L0_3 (solved pops=59 evals=380 maxopen=322) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_7 (solved pops=58 evals=361 maxopen=304) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=23 evals=171 maxopen=149) +[OK ] extrinsic_L0_9 (solved pops=51 evals=358 maxopen=292) +[OK ] extrinsic_L0_8 (solved pops=56 evals=356 maxopen=301) +[OK ] extrinsic_L0_4 (solved pops=199 evals=1060 maxopen=862) +[OK ] extrinsic_L1_4 (solved pops=16 evals=116 maxopen=99) +[OK ] extrinsic_L0_11 (solved pops=205 evals=1107 maxopen=903) +[OK ] extrinsic_L1_1 (solved pops=235 evals=1257 maxopen=1005) +[OK ] extrinsic_L1_2 (solved pops=426 evals=2252 maxopen=1827) +[OK ] extrinsic_L1_3 (solved pops=427 evals=2266 maxopen=1840) +[OK ] extrinsic_L2_1 (solved pops=1279 evals=7100 maxopen=5822) +[OK ] extrinsic_L2_6 (solved pops=1551 evals=8821 maxopen=7271) +[OK ] extrinsic_L2_7 (solved pops=1002 evals=5652 maxopen=4651) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26139 maxopen=22140) +[ ] extrinsic_L0_14 (budget pops=4000 evals=26318 maxopen=22319) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25982 maxopen=21983) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25977 maxopen=21978) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25802 maxopen=21803) +[OK ] extrinsic_L2_9 (solved pops=930 evals=5227 maxopen=4298) +[OK ] extrinsic_L2_12 (solved pops=1290 evals=7169 maxopen=5880) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26308 maxopen=22309) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26304 maxopen=22305) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25747 maxopen=21748) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25980 maxopen=21981) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25766 maxopen=21767) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25768 maxopen=21769) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25981 maxopen=21982) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26025 maxopen=22026) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25803 maxopen=21804) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25917 maxopen=21918) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26144 maxopen=22145) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26205 maxopen=22206) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26075 maxopen=22076) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25893 maxopen=21894) +[OK ] extrinsic_L3_13 (solved pops=3171 evals=19512 maxopen=16342) +[OK ] extrinsic_L3_14 (solved pops=3297 evals=21359 maxopen=18063) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25900 maxopen=21901) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26223 maxopen=22224) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26211 maxopen=22212) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25917 maxopen=21918) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25980 maxopen=21981) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25973 maxopen=21974) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26102 maxopen=22103) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26166 maxopen=22167) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25995 maxopen=21996) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26252 maxopen=22253) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26199 maxopen=22200) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26989 maxopen=22990) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26070 maxopen=22071) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26040 maxopen=22041) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26110 maxopen=22111) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26600 maxopen=22601) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26899 maxopen=22900) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26901 maxopen=22902) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26030 maxopen=22031) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25957 maxopen=21958) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26149 maxopen=22150) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25959 maxopen=21960) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26711 maxopen=22712) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26163 maxopen=22164) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26527 maxopen=22528) +[OK ] extrinsic_L4_12 (solved pops=1324 evals=7459 maxopen=6133) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25582 maxopen=21583) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26397 maxopen=22398) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26098 maxopen=22099) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26347 maxopen=22348) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26486 maxopen=22487) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26213 maxopen=22214) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26269 maxopen=22270) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26414 maxopen=22415) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26486 maxopen=22487) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26303 maxopen=22304) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26420 maxopen=22421) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26433 maxopen=22434) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26563 maxopen=22564) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26793 maxopen=22794) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26145 maxopen=22146) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31150 maxopen=27151) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31131 maxopen=27132) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31113 maxopen=27114) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30997 maxopen=26998) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31065 maxopen=27066) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26062 maxopen=22063) +[ ] extrinsic_L6_7 (budget pops=4000 evals=26000 maxopen=22001) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31119 maxopen=27120) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31296 maxopen=27297) +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_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..d52468e46b854d8f551bd3b8968dc802be837053 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/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 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(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_6 (solved pops=49 evals=312 maxopen=264) +[OK ] extrinsic_L0_2 (solved pops=48 evals=296 maxopen=249) +[OK ] extrinsic_L0_3 (solved pops=60 evals=390 maxopen=331) +[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_12 (solved pops=10 evals=78 maxopen=52) +[OK ] extrinsic_L0_9 (solved pops=46 evals=308 maxopen=247) +[OK ] extrinsic_L0_13 (solved pops=26 evals=180 maxopen=155) +[OK ] extrinsic_L0_7 (solved pops=71 evals=423 maxopen=353) +[OK ] extrinsic_L0_8 (solved pops=69 evals=418 maxopen=350) +[OK ] extrinsic_L0_4 (solved pops=213 evals=1116 maxopen=904) +[OK ] extrinsic_L1_4 (solved pops=16 evals=117 maxopen=100) +[OK ] extrinsic_L0_11 (solved pops=219 evals=1163 maxopen=945) +[OK ] extrinsic_L1_1 (solved pops=261 evals=1373 maxopen=1095) +[OK ] extrinsic_L1_2 (solved pops=513 evals=2741 maxopen=2229) +[OK ] extrinsic_L1_3 (solved pops=511 evals=2733 maxopen=2223) +[OK ] extrinsic_L2_1 (solved pops=1154 evals=6598 maxopen=5445) +[OK ] extrinsic_L2_6 (solved pops=1753 evals=10234 maxopen=8482) +[OK ] extrinsic_L2_7 (solved pops=933 evals=5274 maxopen=4342) +[OK ] extrinsic_L0_14 (solved pops=3733 evals=24501 maxopen=20769) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26005 maxopen=22006) +[ ] extrinsic_L2_3 (budget pops=4000 evals=26045 maxopen=22046) +[OK ] extrinsic_L2_11 (solved pops=26 evals=181 maxopen=154) +[ ] extrinsic_L2_4 (budget pops=4000 evals=26040 maxopen=22041) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25766 maxopen=21767) +[OK ] extrinsic_L2_9 (solved pops=945 evals=5275 maxopen=4331) +[OK ] extrinsic_L2_12 (solved pops=1120 evals=6406 maxopen=5287) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26704 maxopen=22705) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26141 maxopen=22142) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25682 maxopen=21683) +[ ] extrinsic_L3_1 (budget pops=4000 evals=26046 maxopen=22047) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25689 maxopen=21690) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25762 maxopen=21763) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26007 maxopen=22008) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26008 maxopen=22009) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25767 maxopen=21768) +[ ] extrinsic_L3_7 (budget pops=4000 evals=26018 maxopen=22019) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26075 maxopen=22076) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26228 maxopen=22229) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26079 maxopen=22080) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25837 maxopen=21838) +[OK ] extrinsic_L3_13 (solved pops=3510 evals=23302 maxopen=19793) +[OK ] extrinsic_L3_14 (solved pops=3493 evals=23860 maxopen=20368) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25803 maxopen=21804) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26072 maxopen=22073) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26057 maxopen=22058) +[ ] extrinsic_L3_17 (budget pops=4000 evals=26101 maxopen=22102) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25141 maxopen=21142) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26185 maxopen=22186) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26276 maxopen=22277) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26061 maxopen=22062) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25961 maxopen=21962) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26025 maxopen=22026) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26510 maxopen=22511) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26267 maxopen=22268) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27340 maxopen=23341) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26326 maxopen=22327) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26110 maxopen=22111) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26578 maxopen=22579) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26420 maxopen=22421) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26111 maxopen=22112) +[ ] extrinsic_L4_2 (budget pops=4000 evals=27020 maxopen=23021) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25924 maxopen=21925) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26290 maxopen=22291) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25932 maxopen=21933) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26726 maxopen=22727) +[OK ] extrinsic_L4_12 (solved pops=1249 evals=7239 maxopen=5988) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26457 maxopen=22458) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26008 maxopen=22009) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25920 maxopen=21921) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26674 maxopen=22675) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25741 maxopen=21742) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26304 maxopen=22305) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25651 maxopen=21652) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26235 maxopen=22236) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26290 maxopen=22291) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25539 maxopen=21540) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26437 maxopen=22438) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26228 maxopen=22229) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26460 maxopen=22461) +[ ] extrinsic_L5_9 (budget pops=4000 evals=25908 maxopen=21909) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26428 maxopen=22429) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26981 maxopen=22982) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31131 maxopen=27132) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25885 maxopen=21886) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31069 maxopen=27070) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30939 maxopen=26940) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31056 maxopen=27057) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30905 maxopen=26906) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25954 maxopen=21955) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25938 maxopen=21939) +[ ] extrinsic_L6_9 (budget pops=4000 evals=26156 maxopen=22157) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31217 maxopen=27218) +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) -> 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+ "outcome": "budget", + "pops_used": 4000, + "evals_used": 25937, + "max_open": 21938, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31281, + "max_open": 27282, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31151, + "max_open": 27152, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..0fd73cc9b65a2a6ea3fc9d15c8e761927b8bcc96 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/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=53 evals=346 maxopen=294) +[OK ] extrinsic_L0_3 (solved pops=57 evals=373 maxopen=317) +[OK ] extrinsic_L0_6 (solved pops=51 evals=342 maxopen=292) +[OK ] extrinsic_L0_5 (solved pops=58 evals=371 maxopen=314) +[OK ] extrinsic_L0_8 (solved pops=55 evals=353 maxopen=299) +[OK ] extrinsic_L0_10 (solved pops=8 evals=56 maxopen=49) +[OK ] extrinsic_L0_7 (solved pops=58 evals=361 maxopen=304) +[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=51 evals=358 maxopen=292) +[OK ] extrinsic_L0_4 (solved pops=199 evals=1060 maxopen=862) +[OK ] extrinsic_L1_4 (solved pops=18 evals=120 maxopen=101) +[OK ] extrinsic_L0_11 (solved pops=205 evals=1107 maxopen=903) +[OK ] extrinsic_L1_1 (solved pops=250 evals=1331 maxopen=1064) +[OK ] extrinsic_L1_2 (solved pops=412 evals=2114 maxopen=1703) +[OK ] extrinsic_L1_3 (solved pops=413 evals=2128 maxopen=1716) +[OK ] extrinsic_L2_1 (solved pops=1263 evals=6976 maxopen=5714) +[OK ] extrinsic_L2_6 (solved pops=1592 evals=9087 maxopen=7496) +[OK ] extrinsic_L2_7 (solved pops=985 evals=5588 maxopen=4604) +[ ] extrinsic_L2_2 (budget pops=4000 evals=26166 maxopen=22167) +[ ] extrinsic_L0_14 (budget pops=4000 evals=26331 maxopen=22332) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25958 maxopen=21959) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25953 maxopen=21954) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25732 maxopen=21733) +[OK ] extrinsic_L2_9 (solved pops=948 evals=5352 maxopen=4405) +[OK ] extrinsic_L2_12 (solved pops=1281 evals=7096 maxopen=5816) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26322 maxopen=22323) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26301 maxopen=22302) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25771 maxopen=21772) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25972 maxopen=21973) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25827 maxopen=21828) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25834 maxopen=21835) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26037 maxopen=22038) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26008 maxopen=22009) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25740 maxopen=21741) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25939 maxopen=21940) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26161 maxopen=22162) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26254 maxopen=22255) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26060 maxopen=22061) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25876 maxopen=21877) +[OK ] extrinsic_L3_13 (solved pops=3107 evals=18509 maxopen=15403) +[OK ] extrinsic_L3_14 (solved pops=3276 evals=20712 maxopen=17437) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25882 maxopen=21883) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26182 maxopen=22183) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25889 maxopen=21890) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26154 maxopen=22155) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25942 maxopen=21943) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25989 maxopen=21990) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26118 maxopen=22119) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26169 maxopen=22170) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26451 maxopen=22452) +[ ] extrinsic_L3_22 (budget pops=4000 evals=26005 maxopen=22006) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26179 maxopen=22180) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27033 maxopen=23034) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26084 maxopen=22085) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26076 maxopen=22077) +[ ] extrinsic_L3_28 (budget pops=4000 evals=26112 maxopen=22113) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26660 maxopen=22661) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26883 maxopen=22884) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26445 maxopen=22446) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26065 maxopen=22066) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25933 maxopen=21934) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26130 maxopen=22131) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25932 maxopen=21933) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26900 maxopen=22901) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26162 maxopen=22163) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26554 maxopen=22555) +[OK ] extrinsic_L4_12 (solved pops=1301 evals=7371 maxopen=6068) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25591 maxopen=21592) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26380 maxopen=22381) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26027 maxopen=22028) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26304 maxopen=22305) +[ ] extrinsic_L5_1 (budget pops=4000 evals=26423 maxopen=22424) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26213 maxopen=22214) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26260 maxopen=22261) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26400 maxopen=22401) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26443 maxopen=22444) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26231 maxopen=22232) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26405 maxopen=22406) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26479 maxopen=22480) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26598 maxopen=22599) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31076 maxopen=27077) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26808 maxopen=22809) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26139 maxopen=22140) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31139 maxopen=27140) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30931 maxopen=26932) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31110 maxopen=27111) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31104 maxopen=27105) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26069 maxopen=22070) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25937 maxopen=21938) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31281 maxopen=27282) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31151 maxopen=27152) +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) -> 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-> ('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_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 26/94 in 2733.9s diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..0a7e07678af602f37fb57b3e34cbb0093f8f21a1 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json @@ -0,0 +1,1365 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/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, + "num_solved": 51, + "elapsed_sec": 2715.7966873645782, + "results": [ + { + "solved": true, + "outcome": "solved", + "pops_used": 2, + "evals_used": 6, + "max_open": 3, + "solution_actions": [ + "intro.", + "intro." + ], + "problem": "extrinsic_L0_1" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 7, + "evals_used": 18, + "max_open": 12, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "c and_el", + "=> (and_el x x0 x1)." + ], + "problem": "extrinsic_L0_2" + }, + { + "solved": true, + "outcome": 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4000, + "evals_used": 79189, + "max_open": 75190, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 79349, + "max_open": 75350, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 674, + "evals_used": 3066, + "max_open": 2393, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "a and_i", + "=> x0; x2.", + "a x3", + "=> x.", + "c and_el", + "=> (and_el x x1 x5).", + "a x4", + "=> x1.", + "c and_er", + "=> (and_er x x1 x5)." + ], + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 23412, + "max_open": 19413, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 89547, + "max_open": 85548, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 115206, + "max_open": 111207, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..73a8d45901fb810e41f69ec416dea485a16ad4d6 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_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=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_7 (solved pops=16 evals=43 maxopen=28) +[OK ] extrinsic_L0_5 (solved pops=7 evals=17 maxopen=11) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[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_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_8 (solved pops=10 evals=29 maxopen=20) +[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_3 (solved pops=12 evals=83 maxopen=53) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L1_2 (solved pops=12 evals=83 maxopen=53) +[OK ] extrinsic_L0_12 (solved pops=24 evals=132 maxopen=92) +[OK ] extrinsic_L2_3 (solved pops=24 evals=126 maxopen=103) +[OK ] extrinsic_L2_1 (solved pops=36 evals=155 maxopen=120) +[OK ] extrinsic_L2_4 (solved pops=28 evals=167 maxopen=140) +[OK ] extrinsic_L2_7 (solved pops=12 evals=44 maxopen=33) +[OK ] extrinsic_L2_6 (solved pops=42 evals=260 maxopen=219) +[OK ] extrinsic_L2_10 (solved pops=11 evals=28 maxopen=18) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_8 (solved pops=24 evals=108 maxopen=85) +[OK ] extrinsic_L2_9 (solved pops=25 evals=119 maxopen=95) +[OK ] extrinsic_L3_1 (solved pops=12 evals=32 maxopen=21) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L3_4 (solved pops=22 evals=130 maxopen=88) +[OK ] extrinsic_L2_12 (solved pops=54 evals=238 maxopen=185) +[OK ] extrinsic_L3_2 (solved pops=48 evals=318 maxopen=271) +[OK ] extrinsic_L3_5 (solved pops=23 evals=145 maxopen=102) +[OK ] extrinsic_L2_5 (solved pops=115 evals=620 maxopen=506) +[OK ] extrinsic_L3_6 (solved pops=91 evals=413 maxopen=323) +[OK ] extrinsic_L2_2 (solved pops=177 evals=952 maxopen=776) +[OK ] extrinsic_L3_11 (solved pops=85 evals=515 maxopen=428) +[OK ] extrinsic_L3_12 (solved pops=81 evals=457 maxopen=377) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=24 evals=119 maxopen=96) +[OK ] extrinsic_L3_15 (solved pops=130 evals=760 maxopen=631) +[OK ] extrinsic_L3_16 (solved pops=43 evals=248 maxopen=206) +[OK ] extrinsic_L3_17 (solved pops=129 evals=729 maxopen=582) +[OK ] extrinsic_L3_18 (solved pops=51 evals=404 maxopen=333) +[OK ] extrinsic_L3_7 (solved pops=952 evals=4324 maxopen=3373) +[ ] extrinsic_L2_13 (budget pops=4000 evals=24659 maxopen=20660) +[ ] extrinsic_L3_9 (budget pops=4000 evals=24710 maxopen=20711) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25405 maxopen=21406) +[OK ] extrinsic_L3_23 (solved pops=68 evals=384 maxopen=317) +[ ] extrinsic_L3_8 (budget pops=4000 evals=30651 maxopen=26652) +[ ] extrinsic_L3_19 (budget pops=4000 evals=23278 maxopen=19279) +[OK ] extrinsic_L3_25 (solved pops=636 evals=4214 maxopen=3559) +[ ] extrinsic_L3_20 (budget pops=4000 evals=22976 maxopen=18977) +[ ] extrinsic_L3_24 (budget pops=4000 evals=28251 maxopen=24252) +[ ] extrinsic_L3_21 (budget pops=4000 evals=22365 maxopen=18366) +[ ] extrinsic_L3_22 (budget pops=4000 evals=21896 maxopen=17897) +[ ] extrinsic_L3_27 (budget pops=4000 evals=32483 maxopen=28484) +[OK ] extrinsic_L4_3 (solved pops=419 evals=1954 maxopen=1536) +[ ] extrinsic_L3_26 (budget pops=4000 evals=31533 maxopen=27534) +[ ] extrinsic_L3_28 (budget pops=4000 evals=32494 maxopen=28495) +[ ] extrinsic_L4_1 (budget pops=4000 evals=27138 maxopen=23139) +[ ] extrinsic_L4_2 (budget pops=4000 evals=39816 maxopen=35817) +[ ] extrinsic_L3_29 (budget pops=4000 evals=32745 maxopen=28746) +[ ] extrinsic_L4_4 (budget pops=4000 evals=38254 maxopen=34255) +[ ] extrinsic_L4_5 (budget pops=4000 evals=44473 maxopen=40474) +[ ] extrinsic_L4_6 (budget pops=4000 evals=38285 maxopen=34286) +[OK ] extrinsic_L4_12 (solved pops=108 evals=642 maxopen=532) +[ ] extrinsic_L4_7 (budget pops=4000 evals=32348 maxopen=28349) +[ ] extrinsic_L4_8 (budget pops=4000 evals=28865 maxopen=24866) +[ ] extrinsic_L4_9 (budget pops=4000 evals=32227 maxopen=28228) +[ ] extrinsic_L4_10 (budget pops=4000 evals=35180 maxopen=31181) +[ ] extrinsic_L4_11 (budget pops=4000 evals=37657 maxopen=33658) +[ ] extrinsic_L4_13 (budget pops=4000 evals=35660 maxopen=31661) +[ ] extrinsic_L4_14 (budget pops=4000 evals=36390 maxopen=32391) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25539 maxopen=21540) +[ ] extrinsic_L5_2 (budget pops=4000 evals=27810 maxopen=23811) +[ ] extrinsic_L5_3 (budget pops=4000 evals=29980 maxopen=25981) +[ ] extrinsic_L5_6 (budget pops=4000 evals=30079 maxopen=26080) +[ ] extrinsic_L5_4 (budget pops=4000 evals=26315 maxopen=22316) +[ ] extrinsic_L5_5 (budget pops=4000 evals=36005 maxopen=32006) +[OK ] extrinsic_L6_1 (solved pops=44 evals=315 maxopen=272) +[ ] extrinsic_L5_7 (budget pops=4000 evals=32295 maxopen=28296) +[ ] extrinsic_L5_8 (budget pops=4000 evals=32717 maxopen=28718) +[ ] extrinsic_L5_9 (budget pops=4000 evals=24972 maxopen=20973) +[ ] extrinsic_L5_10 (budget pops=4000 evals=27700 maxopen=23701) +[OK ] extrinsic_L6_6 (solved pops=674 evals=3066 maxopen=2393) +[ ] extrinsic_L5_11 (budget pops=4000 evals=112556 maxopen=108557) +[ ] extrinsic_L6_2 (timeout pops=3746 evals=61834 maxopen=58089) +[ ] extrinsic_L6_3 (timeout pops=3799 evals=64506 maxopen=60708) +[ ] extrinsic_L6_4 (budget pops=4000 evals=79189 maxopen=75190) +[ ] extrinsic_L6_7 (budget pops=4000 evals=23412 maxopen=19413) +[ ] extrinsic_L6_5 (budget pops=4000 evals=79349 maxopen=75350) +[ ] extrinsic_L6_9 (budget pops=4000 evals=115206 maxopen=111207) +[ ] extrinsic_L6_8 (budget pops=4000 evals=89547 maxopen=85548) +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) 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-> '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=11 evals=53 maxopen=43) +[OK ] extrinsic_L0_2 (solved pops=15 evals=92 maxopen=78) +[OK ] extrinsic_L0_4 (solved pops=11 evals=39 maxopen=29) +[OK ] extrinsic_L0_5 (solved pops=13 evals=56 maxopen=44) +[OK ] extrinsic_L0_6 (solved pops=11 evals=53 maxopen=43) +[OK ] extrinsic_L0_9 (solved pops=11 evals=69 maxopen=43) +[OK ] extrinsic_L0_10 (solved pops=6 evals=13 maxopen=8) +[OK ] extrinsic_L0_8 (solved pops=20 evals=130 maxopen=111) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_12 (solved pops=12 evals=55 maxopen=27) +[OK ] extrinsic_L0_11 (solved pops=14 evals=59 maxopen=46) +[OK ] extrinsic_L0_7 (solved pops=23 evals=151 maxopen=129) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_1 (solved pops=21 evals=147 maxopen=109) +[OK ] extrinsic_L1_2 (solved pops=32 evals=240 maxopen=190) +[OK ] extrinsic_L1_3 (solved pops=32 evals=239 maxopen=189) +[OK ] extrinsic_L0_14 (solved pops=52 evals=355 maxopen=304) +[OK ] extrinsic_L2_1 (solved pops=87 evals=502 maxopen=416) +[OK ] extrinsic_L2_7 (solved pops=38 evals=263 maxopen=226) +[OK ] extrinsic_L2_3 (solved pops=108 evals=735 maxopen=628) +[OK ] extrinsic_L2_4 (solved pops=111 evals=741 maxopen=631) +[OK ] extrinsic_L2_6 (solved pops=109 evals=698 maxopen=590) +[OK ] extrinsic_L2_11 (solved pops=8 evals=32 maxopen=23) +[OK ] extrinsic_L2_10 (solved pops=71 evals=515 maxopen=445) +[OK ] extrinsic_L2_8 (solved pops=96 evals=590 maxopen=495) +[OK ] extrinsic_L2_9 (solved pops=95 evals=595 maxopen=501) +[OK ] extrinsic_L2_12 (solved pops=95 evals=535 maxopen=441) +[OK ] extrinsic_L3_3 (solved pops=50 evals=378 maxopen=329) +[OK ] extrinsic_L3_1 (solved pops=79 evals=544 maxopen=466) +[OK ] extrinsic_L3_4 (solved pops=83 evals=606 maxopen=503) +[OK ] extrinsic_L3_5 (solved pops=84 evals=615 maxopen=511) +[OK ] extrinsic_L3_2 (solved pops=486 evals=2225 maxopen=1740) +[OK ] extrinsic_L2_2 (solved pops=871 evals=4004 maxopen=3134) +[OK ] extrinsic_L2_5 (solved pops=882 evals=4035 maxopen=3154) +[OK ] extrinsic_L3_6 (solved pops=802 evals=3590 maxopen=2789) +[OK ] extrinsic_L3_11 (solved pops=249 evals=1298 maxopen=1047) +[OK ] extrinsic_L3_12 (solved pops=463 evals=2106 maxopen=1644) +[OK ] extrinsic_L3_13 (solved pops=40 evals=297 maxopen=258) +[OK ] extrinsic_L3_14 (solved pops=79 evals=532 maxopen=454) +[ ] extrinsic_L2_13 (budget pops=4000 evals=26719 maxopen=22720) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25161 maxopen=21162) +[OK ] extrinsic_L3_15 (solved pops=2474 evals=15986 maxopen=13513) +[OK ] extrinsic_L3_16 (solved pops=237 evals=1235 maxopen=999) +[OK ] extrinsic_L3_18 (solved pops=559 evals=2608 maxopen=2029) +[ ] extrinsic_L3_8 (budget pops=4000 evals=24606 maxopen=20607) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26778 maxopen=22779) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26090 maxopen=22091) +[OK ] extrinsic_L3_23 (solved pops=835 evals=3987 maxopen=3153) +[OK ] extrinsic_L3_17 (solved pops=2071 evals=11556 maxopen=9467) +[OK ] extrinsic_L3_25 (solved pops=1124 evals=5483 maxopen=4340) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26825 maxopen=22826) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25262 maxopen=21263) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25596 maxopen=21597) +[ ] extrinsic_L3_20 (budget pops=4000 evals=25829 maxopen=21830) +[ ] extrinsic_L3_24 (budget pops=4000 evals=25491 maxopen=21492) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25165 maxopen=21166) +[ ] extrinsic_L3_27 (budget pops=4000 evals=25025 maxopen=21026) +[OK ] extrinsic_L4_3 (solved pops=1420 evals=6791 maxopen=5372) +[ ] extrinsic_L4_1 (budget pops=4000 evals=25393 maxopen=21394) +[ ] extrinsic_L3_28 (budget pops=4000 evals=24995 maxopen=20996) +[ ] extrinsic_L4_2 (budget pops=4000 evals=32373 maxopen=28374) +[ ] extrinsic_L3_29 (budget pops=4000 evals=29308 maxopen=25309) +[ ] extrinsic_L4_4 (budget pops=4000 evals=26984 maxopen=22985) +[ ] extrinsic_L4_6 (budget pops=4000 evals=26792 maxopen=22793) +[ ] extrinsic_L4_5 (budget pops=4000 evals=29111 maxopen=25112) +[OK ] extrinsic_L4_12 (solved pops=233 evals=1159 maxopen=924) +[ ] extrinsic_L4_7 (budget pops=4000 evals=24402 maxopen=20403) +[ ] extrinsic_L4_8 (budget pops=4000 evals=27467 maxopen=23468) +[ ] extrinsic_L4_9 (budget pops=4000 evals=25192 maxopen=21193) +[ ] extrinsic_L4_10 (budget pops=4000 evals=28259 maxopen=24260) +[ ] extrinsic_L4_11 (budget pops=4000 evals=31615 maxopen=27616) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25657 maxopen=21658) +[ ] extrinsic_L4_14 (budget pops=4000 evals=24994 maxopen=20995) +[ ] extrinsic_L5_1 (budget pops=4000 evals=28737 maxopen=24738) +[ ] extrinsic_L5_2 (budget pops=4000 evals=28520 maxopen=24521) +[ ] extrinsic_L5_3 (budget pops=4000 evals=28077 maxopen=24078) +[ ] extrinsic_L5_6 (budget pops=4000 evals=24067 maxopen=20068) +[ ] extrinsic_L5_5 (budget pops=4000 evals=27524 maxopen=23525) +[ ] extrinsic_L5_4 (budget pops=4000 evals=28919 maxopen=24920) +[OK ] extrinsic_L6_1 (solved pops=375 evals=1861 maxopen=1487) +[ ] extrinsic_L5_7 (budget pops=4000 evals=27713 maxopen=23714) +[ ] extrinsic_L5_8 (budget pops=4000 evals=30599 maxopen=26600) +[ ] extrinsic_L5_11 (budget pops=4000 evals=35729 maxopen=31730) +[ ] extrinsic_L5_9 (budget pops=4000 evals=28630 maxopen=24631) +[ ] extrinsic_L5_10 (budget pops=4000 evals=29849 maxopen=25850) +[ ] extrinsic_L6_2 (budget pops=4000 evals=44337 maxopen=40338) +[ ] extrinsic_L6_3 (budget pops=4000 evals=44295 maxopen=40296) +[ ] extrinsic_L6_4 (budget pops=4000 evals=59781 maxopen=55782) +[ ] extrinsic_L6_5 (budget pops=4000 evals=44500 maxopen=40501) +[ ] extrinsic_L6_7 (budget pops=4000 evals=24799 maxopen=20800) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25447 maxopen=21448) +[ ] extrinsic_L6_9 (budget pops=4000 evals=29365 maxopen=25366) +[ ] extrinsic_L6_8 (budget pops=4000 evals=43452 maxopen=39453) +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) 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4000, + "evals_used": 25641, + "max_open": 21642, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 44146, + "max_open": 40147, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 35299, + "max_open": 31300, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..719b281301e284c7ad3bac757b9e896a9e177c34 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/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_2 (solved pops=14 evals=74 maxopen=61) +[OK ] extrinsic_L0_3 (solved pops=10 evals=37 maxopen=28) +[OK ] extrinsic_L0_4 (solved pops=12 evals=55 maxopen=44) +[OK ] extrinsic_L0_5 (solved pops=13 evals=56 maxopen=44) +[OK ] extrinsic_L0_6 (solved pops=10 evals=37 maxopen=28) +[OK ] extrinsic_L0_8 (solved pops=16 evals=94 maxopen=79) +[OK ] extrinsic_L0_7 (solved pops=22 evals=137 maxopen=116) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=11 evals=69 maxopen=43) +[OK ] extrinsic_L0_11 (solved pops=10 evals=51 maxopen=42) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_12 (solved pops=16 evals=63 maxopen=31) +[OK ] extrinsic_L1_1 (solved pops=16 evals=97 maxopen=64) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L0_14 (solved pops=45 evals=312 maxopen=268) +[OK ] extrinsic_L1_3 (solved pops=32 evals=220 maxopen=189) +[OK ] extrinsic_L1_2 (solved pops=32 evals=221 maxopen=190) +[OK ] extrinsic_L2_1 (solved pops=82 evals=474 maxopen=393) +[OK ] extrinsic_L2_4 (solved pops=80 evals=553 maxopen=474) +[OK ] extrinsic_L2_3 (solved pops=81 evals=557 maxopen=477) +[OK ] extrinsic_L2_7 (solved pops=33 evals=211 maxopen=179) +[OK ] extrinsic_L2_6 (solved pops=104 evals=644 maxopen=541) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=56 evals=378 maxopen=323) +[OK ] extrinsic_L2_10 (solved pops=63 evals=459 maxopen=397) +[OK ] extrinsic_L2_8 (solved pops=83 evals=527 maxopen=445) +[OK ] extrinsic_L3_1 (solved pops=55 evals=443 maxopen=389) +[OK ] extrinsic_L2_12 (solved pops=98 evals=551 maxopen=454) +[OK ] extrinsic_L3_3 (solved pops=45 evals=322 maxopen=278) +[OK ] extrinsic_L3_4 (solved pops=75 evals=578 maxopen=483) +[OK ] extrinsic_L3_5 (solved pops=74 evals=567 maxopen=473) +[OK ] extrinsic_L3_2 (solved pops=381 evals=1732 maxopen=1352) +[OK ] extrinsic_L2_5 (solved pops=741 evals=3220 maxopen=2480) +[OK ] extrinsic_L2_2 (solved pops=779 evals=3484 maxopen=2706) +[OK ] extrinsic_L3_6 (solved pops=675 evals=3005 maxopen=2331) +[OK ] extrinsic_L3_11 (solved pops=270 evals=1355 maxopen=1083) +[OK ] extrinsic_L3_12 (solved pops=524 evals=2416 maxopen=1893) +[OK ] extrinsic_L3_13 (solved pops=36 evals=259 maxopen=224) +[OK ] extrinsic_L3_14 (solved pops=53 evals=385 maxopen=333) +[OK ] extrinsic_L3_15 (solved pops=1649 evals=8278 maxopen=6630) +[OK ] extrinsic_L3_16 (solved pops=154 evals=904 maxopen=751) +[ ] extrinsic_L2_13 (budget pops=4000 evals=27234 maxopen=23235) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25231 maxopen=21232) +[OK ] extrinsic_L3_18 (solved pops=386 evals=1860 maxopen=1454) +[OK ] extrinsic_L3_17 (solved pops=1532 evals=7744 maxopen=6194) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25784 maxopen=21785) +[ ] extrinsic_L3_9 (budget pops=4000 evals=27863 maxopen=23864) +[ ] extrinsic_L3_10 (budget pops=4000 evals=27086 maxopen=23087) +[OK ] extrinsic_L3_23 (solved pops=660 evals=2892 maxopen=2233) +[OK ] extrinsic_L3_25 (solved pops=1083 evals=5414 maxopen=4312) +[ ] extrinsic_L3_19 (budget pops=4000 evals=27419 maxopen=23420) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26727 maxopen=22728) +[ ] extrinsic_L3_24 (budget pops=4000 evals=25994 maxopen=21995) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25593 maxopen=21594) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26820 maxopen=22821) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26387 maxopen=22388) +[OK ] extrinsic_L4_3 (solved pops=801 evals=3654 maxopen=2854) +[ ] extrinsic_L3_27 (budget pops=4000 evals=25629 maxopen=21630) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26118 maxopen=22119) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25237 maxopen=21238) +[ ] extrinsic_L4_2 (budget pops=4000 evals=33015 maxopen=29016) +[ ] extrinsic_L3_29 (budget pops=4000 evals=27374 maxopen=23375) +[ ] extrinsic_L4_4 (budget pops=4000 evals=28360 maxopen=24361) +[ ] extrinsic_L4_6 (budget pops=4000 evals=28176 maxopen=24177) +[ ] extrinsic_L4_5 (budget pops=4000 evals=29093 maxopen=25094) +[OK ] extrinsic_L4_12 (solved pops=177 evals=986 maxopen=807) +[ ] extrinsic_L4_7 (budget pops=4000 evals=24661 maxopen=20662) +[ ] extrinsic_L4_8 (budget pops=4000 evals=28174 maxopen=24175) +[ ] extrinsic_L4_9 (budget pops=4000 evals=24972 maxopen=20973) +[ ] extrinsic_L4_10 (budget pops=4000 evals=26894 maxopen=22895) +[ ] extrinsic_L4_11 (budget pops=4000 evals=31756 maxopen=27757) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26131 maxopen=22132) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26386 maxopen=22387) +[ ] extrinsic_L5_1 (budget pops=4000 evals=28231 maxopen=24232) +[ ] extrinsic_L5_2 (budget pops=4000 evals=29350 maxopen=25351) +[ ] extrinsic_L5_3 (budget pops=4000 evals=28789 maxopen=24790) +[ ] extrinsic_L5_6 (budget pops=4000 evals=24598 maxopen=20599) +[ ] extrinsic_L5_5 (budget pops=4000 evals=27285 maxopen=23286) +[ ] extrinsic_L5_4 (budget pops=4000 evals=28257 maxopen=24258) +[OK ] extrinsic_L6_1 (solved pops=325 evals=1647 maxopen=1323) +[ ] extrinsic_L5_7 (budget pops=4000 evals=27772 maxopen=23773) +[ ] extrinsic_L5_8 (budget pops=4000 evals=29006 maxopen=25007) +[ ] extrinsic_L5_9 (budget pops=4000 evals=27800 maxopen=23801) +[ ] extrinsic_L5_11 (budget pops=4000 evals=29023 maxopen=25024) +[ ] extrinsic_L5_10 (budget pops=4000 evals=28335 maxopen=24336) +[ ] extrinsic_L6_2 (budget pops=4000 evals=44659 maxopen=40660) +[ ] extrinsic_L6_3 (budget pops=4000 evals=44709 maxopen=40710) +[ ] extrinsic_L6_4 (budget pops=4000 evals=38764 maxopen=34765) +[ ] extrinsic_L6_5 (budget pops=4000 evals=38003 maxopen=34004) +[ ] extrinsic_L6_6 (budget pops=4000 evals=26530 maxopen=22531) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25641 maxopen=21642) +[ ] extrinsic_L6_9 (budget pops=4000 evals=35299 maxopen=31300) +[ ] extrinsic_L6_8 (budget pops=4000 evals=44146 maxopen=40147) +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_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 49/94 in 2114.5s